Simple Harmonic Motion

157 questions · Physics · JEE Main

Simple Harmonic Motion

157 questions · Physics · JEE Main

A particle is subjected to two simple harmonic motions as : $x_{1} = 7 sin 5 tcm$ and $x_{2} = 27 sin (5 t + \frac{π}{3}) cm$ where $x$ is displacement and $t$ is time in seconds. The maximum…2025 · 2 Apr · Shift 1 · Q59 · MCQ
Two blocks of masses $m$ and $M, (M > m)$ , are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $μ =$ … Includes diagram2025 · 3 Apr · Shift 1 · Q65 · MCQ
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $θ_{1}$ and $θ_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then…2025 · 4 Apr · Shift 1 · Q53 · MCQ
A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The…2025 · 8 Apr · Shift 2 · Q69 · MCQ
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The…2025 · 22 Jan · Shift 2 · Q51 · MCQ
A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y π \times 1 0^{- 2} s$ , where the value…2025 · 23 Jan · Shift 1 · Q60 · MCQ
A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then $\frac{D}{d}$ is2025 · 24 Jan · Shift 1 · Q57 · MCQ
A particle oscillates along the $x$ -axis according to the law, $x (t) = x_{0} sin^{2} (\frac{t}{2})$ where $x_{0} = 1 m$ . The kinetic energy $(K)$ of the particle as a function of $x$ is correctly…2025 · 24 Jan · Shift 2 · Q70 · MCQ
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position $x_{0}$ and initial momentum $p_{0}$ is enough to determine the position and momentum…2025 · 28 Jan · Shift 2 · Q69 · MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R)…2025 · 29 Jan · Shift 1 · Q57 · MCQ
Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the…2025 · 29 Jan · Shift 2 · Q60 · MCQ
A simple pendulum of length $1 m$ has a wooden bob of mass $1 kg$ . It is struck by a bullet of mass $1 0^{- 2} kg$ moving with a speed of $2 \times 1 0^{2} ms^{- 1}$ . The bullet gets embedded into the bob.…2024 · 1 Feb · Shift 1 · Q75 · MCQ
A mass $m$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_{1}$ . The frequency of oscillations if a mass $9 m$ is suspended from the same spring is $f_{2}$ . The value of $\frac{f _{1}}{f _{2}} i$ …2024 · 1 Feb · Shift 2 · Q81 · Numerical
In simple harmonic motion, the total mechanical energy of given system is $E$ . If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is: Includes diagram2024 · 4 Apr · Shift 2 · Q67 · MCQ
The displacement of a particle executing SHM is given by $x = 10 sin (w t + \frac{π}{3}) m$ . The time period of motion is $3.14 s$ . The velocity of the particle at $t = 0$ is $m / s$ …2024 · 4 Apr · Shift 2 · Q89 · Numerical
A simple pendulum doing small oscillations at a place $R$ height above earth surface has time period of $T_{1} = 4 s$ . $T_{2}$ would be it's time period if it is brought to a point which is at a height $2 R$ from…2024 · 5 Apr · Shift 1 · Q66 · MCQ
A particle is doing simple harmonic motion of amplitude $0.06 m$ and time period $3.14 s$ . The maximum velocity of the particle is $cm / s$ .2024 · 6 Apr · Shift 1 · Q83 · Numerical
An object of mass $0.2 kg$ executes simple harmonic motion along $x$ axis with frequency of $(\frac{25}{π}) Hz$ . At the position $x = 0.04 m$ the object has kinetic energy $0.5 J$ and…2024 · 8 Apr · Shift 2 · Q85 · Numerical
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 m, 2 ms^{- 1}$ and $16 ms^{- 2}$ at a certain instant. The amplitude of the motion is $x, m$ …2024 · 9 Apr · Shift 1 · Q86 · Numerical
A particle of mass $0.50 kg$ executes simple harmonic motion under force $F = - 50 (Nm^{- 1}) x$ . The time period of oscillation is $\frac{x}{35} s$ . The value of $x$ is . (Given $π = \frac{22}{7}$ )2024 · 9 Apr · Shift 2 · Q86 · Numerical
A particle executes simple harmonic motion with an amplitude of $4 cm$ . At the mean position, velocity of the particle is $10 cm / s$ . The distance of the particle from the mean position when its speed becomes $5 cm / s$ …2024 · 27 Jan · Shift 1 · Q87 · Numerical
When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$ , where $x =$ .2024 · 29 Jan · Shift 1 · Q88 · Numerical
The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 m$ . If it dissipates $10%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point…2024 · 29 Jan · Shift 2 · Q75 · MCQ
A simple harmonic oscillator has an amplitude $A$ and time period $6 π$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x =$ A to $x = \frac{3}{2}$ A will be $\frac{π}{x} s$ …2024 · 29 Jan · Shift 2 · Q86 · Numerical
A particle performs simple harmonic motion with amplitude $A$ . Its speed is increased to three times at an instant when its displacement is $\frac{2 A}{3}$ . The new amplitude of motion is $\frac{n A}{3}$ . The value of $n$ is …2024 · 31 Jan · Shift 1 · Q86 · Numerical
The time period of simple harmonic motion of mass $M$ in the given figure is $π \frac{α M}{5 k}$ , where the value of $α$ is . Includes diagram2024 · 31 Jan · Shift 2 · Q90 · Numerical
The amplitude of a particle executing SHM is $3 cm$ . The displacement at which its kinetic energy will be $25%$ more than the potential energy is: $cm$ 2023 · 1 Feb · Shift 1 · Q70 · Numerical
Choose the correct length (L) versus square of the time period ( $T^{2}$ ) graph for a simple pendulum executing simple harmonic motion.2023 · 1 Feb · Shift 2 · Q53 · MCQ
A mass $m$ is attached to two strings as shown in figure. The spring constants of two springs are $K_{1}$ and $K_{2}$ . For the frictionless surface, the time period of oscillation of mass $m$ is : Includes diagram2023 · 6 Apr · Shift 1 · Q55 · MCQ
A simple pendulum with length $100 cm$ and bob of mass $250 g$ is executing S.H.M. of amplitude $10 cm$ . The maximum tension in the string is found to be $\frac{x}{40} N$ . The value of $x$ is …2023 · 6 Apr · Shift 2 · Q70 · Numerical
For particle P revolving round the centre O with radius of circular path $r$ and angular velocity $ω$ , as shown in below figure, the projection of OP on the $x$ -axis at time $t$ is Includes diagram2023 · 8 Apr · Shift 2 · Q44 · MCQ
A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $x = \frac{A}{2}$ and it moves along positive x-axis. The displacement of particle in time t is $x = A sin (w t + δ)$ , then the value of $δ$ …2023 · 10 Apr · Shift 1 · Q54 · MCQ
A rectangular block of mass $5 kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1 m$ and time period $3.14 s$ . The maximum force exerted by spring on block is …2023 · 10 Apr · Shift 2 · Q59 · Numerical
The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position (A) is given by2023 · 11 Apr · Shift 1 · Q57 · MCQ
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be2023 · 12 Apr · Shift 1 · Q44 · MCQ
Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?2023 · 13 Apr · Shift 1 · Q45 · MCQ
At a given point of time the value of displacement of a simple harmonic oscillator is given as $y = A cos (3 0^{\circ})$ . If amplitude is $40 cm$ and kinetic energy at that time is $200 J$ ,…2023 · 13 Apr · Shift 1 · Q69 · Numerical
A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :2023 · 13 Apr · Shift 2 · Q60 · MCQ
In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite in direction. (C) The velocity is maximum at mean position. (D) The acceleration…2023 · 15 Apr · Shift 1 · Q50 · MCQ
A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced… Includes diagram2023 · 24 Jan · Shift 1 · Q64 · Numerical
A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is kg.2023 · 24 Jan · Shift 2 · Q72 · Numerical
T is the time period of simple pendulum on the earth's surface. Its time period becomes $x$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be :2023 · 25 Jan · Shift 1 · Q53 · MCQ
A particle executes simple harmonic motion between $x = - A$ and $x = + A$ . If time taken by particle to go from $x = 0$ to $\frac{A}{2}$ is 2 s; then time taken by particle in going from $x = \frac{A}{2}$ to A is2023 · 25 Jan · Shift 2 · Q48 · MCQ
A particle of mass 250 g executes a simple harmonic motion under a periodic force $F = (- 25 x) N$ . The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is …2023 · 29 Jan · Shift 2 · Q65 · Numerical
The general displacement of a simple harmonic oscillator is $x = A sin ω t$ . Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t = \frac{T}{β}$ . The value of $β$ is …2023 · 30 Jan · Shift 1 · Q61 · Numerical
For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1 kg$ , the angular frequency is $ω_{1}$ . When the mass block is $2 kg$ the angular frequency… Includes diagram2023 · 30 Jan · Shift 2 · Q61 · MCQ
The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2} = 50 - x^{2}$ . The time period of oscillations is $\frac{x}{7} s$ . The value of $x$ is . $($ Take $π = \frac{22}{7})$ …2023 · 30 Jan · Shift 2 · Q67 · Numerical
The maximum potential energy of a block executing simple harmonic motion is $25 J$ . A is amplitude of oscillation. At $A/2$ , the kinetic energy of the block is2023 · 31 Jan · Shift 1 · Q59 · MCQ
In the figure given below, a block of mass $M = 490 g$ placed on a frictionless table is connected with two springs having same spring constant $(K = 2 N m^{- 1})$ . If the block is… Includes diagram2023 · 31 Jan · Shift 1 · Q67 · Numerical
Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will…2022 · 24 Jun · Shift 2 · Q50 · MCQ
In figure $(A)$ , mass ' $2 m^{’}$ is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$ . In figure (B), mass ' $m$ ' is attached to two springs of spring constant… Includes diagram2022 · 25 Jul · Shift 1 · Q49 · MCQ
When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :2022 · 26 Jul · Shift 1 · Q55 · MCQ
As per given figures, two springs of spring constants $k$ and $2 k$ are connected to mass $m$ . If the period of oscillation in figure (a) is $3 s$ , then the period of oscillation in figure (b) will be $x s$ . The value of $x$ … Includes diagram2022 · 26 Jul · Shift 2 · Q65 · Numerical
Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $\frac{g}{6}$ vertically upwards then the time period will be : (Where g = acceleration due to gravity)2022 · 26 Jun · Shift 1 · Q48 · MCQ
A mass $0.9 kg$ , attached to a horizontal spring, executes SHM with an amplitude $A_{1}$ . When this mass passes through its mean position, then a smaller mass of $124 g$ is placed over it and both masses move…2022 · 27 Jul · Shift 1 · Q69 · Numerical
The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :2022 · 27 Jun · Shift 1 · Q56 · MCQ
The equation of a particle executing simple harmonic motion is given by $x = sin π (t + \frac{1}{3}) m$ . At t = 1s, the speed of particle will be (Given : $π$ = 3.14)2022 · 27 Jun · Shift 2 · Q54 · MCQ
A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is …2022 · 27 Jun · Shift 2 · Q66 · Numerical
Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s…2022 · 28 Jul · Shift 2 · Q45 · MCQ
The potential energy of a particle of mass $4 kg$ in motion along the x-axis is given by $U = 4 (1 - cos 4 x)$ J. The time period of the particle for small oscillation $(sin θ ≃ θ)$ is $(\frac{π}{K}) s$ …2022 · 28 Jul · Shift 2 · Q61 · Numerical
Motion of a particle in x-y plane is described by a set of following equations $x = 4 sin (\frac{π}{2} - ω t) m$ and $y = 4 sin (ω t) m$ . The path of the particle will be :2022 · 28 Jun · Shift 1 · Q45 · MCQ
A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60 $^{\circ}$ with vertical as shown in the figure. After releasing the bob, the maximum… Includes diagram2022 · 28 Jun · Shift 1 · Q60 · Numerical
The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $α$ , is given by :2022 · 29 Jul · Shift 1 · Q56 · MCQ
The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $10 s$ . If the metallic bob is immersed in water, then the new time period becomes $5 x$ s. The value of $x$ will be …2022 · 29 Jul · Shift 2 · Q67 · Numerical
A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is $x$ cm. The value of x is …2022 · 29 Jun · Shift 1 · Q62 · Numerical
The motion of a simple pendulum executing S.H.M. is represented by the following equation. $y = A sin (π t + ϕ)$ , where time is measured in second. The length of pendulum is2022 · 29 Jun · Shift 2 · Q53 · MCQ
A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What… Includes diagram2021 · 1 Sep · Shift 2 · Q61 · MCQ
Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be :2021 · 16 Mar · Shift 1 · Q48 · MCQ
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?2021 · 17 Mar · Shift 1 · Q54 · MCQ
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is… Includes diagram2021 · 17 Mar · Shift 1 · Q67 · Numerical
Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is2021 · 17 Mar · Shift 2 · Q53 · MCQ
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a}$ s. The value of 'a' to the nearest integer…2021 · 18 Mar · Shift 1 · Q62 · Numerical
The time period of a simple pendulum is given by $T = 2 π \frac{l}{g}$ . The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a…2021 · 18 Mar · Shift 1 · Q71 · MCQ
The function of time representing a simple harmonic motion with a period of $\frac{π}{ω}$ is :2021 · 18 Mar · Shift 2 · Q56 · MCQ
A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as :2021 · 20 Jul · Shift 2 · Q54 · MCQ
T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is :2021 · 22 Jul · Shift 2 · Q62 · MCQ
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When… Includes diagram2021 · 24 Feb · Shift 1 · Q46 · MCQ
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given… Includes diagram2021 · 24 Feb · Shift 2 · Q42 · MCQ
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :2021 · 24 Feb · Shift 2 · Q50 · MCQ
The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of…2021 · 24 Feb · Shift 2 · Q51 · MCQ
If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :2021 · 25 Feb · Shift 1 · Q57 · MCQ
Y = A sin( $ω$ t + $ϕ$ 0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is $Y = \frac{A}{2}$ and it is moving along negative x-direction. Then the initial phase angle $ϕ$ 0 will be:2021 · 25 Feb · Shift 2 · Q60 · MCQ
Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of… Includes diagram2021 · 25 Feb · Shift 2 · Q61 · MCQ
The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30 $^{\circ}$ in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The… Includes diagram2021 · 25 Feb · Shift 2 · Q62 · MCQ
In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be… Includes diagram2021 · 25 Jul · Shift 1 · Q66 · Numerical
A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 $^{\circ}$ to the vertical will be (g = 10 m/s2) m/s.2021 · 25 Jul · Shift 1 · Q70 · Numerical
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.2021 · 25 Jul · Shift 2 · Q48 · MCQ
Two simple harmonic motions are represented by the equations $x_{1} = 5 sin (2 π t + \frac{π}{4})$ and $x_{2} = 52 (sin 2 π t + cos 2 π t)$ . The amplitude of second motion is ................ times the…2021 · 26 Aug · Shift 2 · Q68 · Numerical
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it…2021 · 26 Feb · Shift 1 · Q51 · MCQ
If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :2021 · 26 Feb · Shift 1 · Q53 · MCQ
A particle executes S.H.M., the graph of velocity as a function of displacement is :2021 · 26 Feb · Shift 2 · Q64 · MCQ
Given below are two statements : Statement I : A second's pendulum has a time period of 1 second. Statement II : It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the…2021 · 26 Feb · Shift 2 · Q66 · MCQ
A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $\frac{x a}{2}$ . The value of x is .2021 · 26 Feb · Shift 2 · Q68 · Numerical
Time period of a simple pendulum is T. The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{α}{β} T$ . The value of $α$ is .2021 · 26 Feb · Shift 2 · Q69 · Numerical
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure : Includes diagram2021 · 27 Aug · Shift 1 · Q58 · MCQ
Two simple harmonic motion, are represented by the equations $y_{1} = 10 sin (3 π t + \frac{π}{3})$ $y_{2} = 5 (sin 3 π t + 3 cos 3 π t)$ Ratio of amplitude of y1 to y2 = x : 1. The value of x is …2021 · 27 Aug · Shift 2 · Q59 · Numerical
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $\frac{3 E}{4}$ then its displacement 'y' is given by :2021 · 27 Jul · Shift 1 · Q60 · MCQ
An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $t = \frac{T}{4} s$ starting from mean position. Assume that the…2021 · 27 Jul · Shift 2 · Q49 · MCQ
A particle executes simple harmonic motion represented by displacement function as x(t) = A sin( $ω$ t + $ϕ$ ) If the position and velocity of the particle at t = 0 s are 2 cm and 2 $ω$ cm s $-$ 1 respectively, then its…2021 · 27 Jul · Shift 2 · Q66 · Numerical
A particle of mass 1 kg is hanging from a spring of force constant 100 Nm $-$ 1. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and…2021 · 31 Aug · Shift 1 · Q65 · Numerical
A bob of mass 'm' suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is…2021 · 31 Aug · Shift 2 · Q51 · MCQ
For a body executing S.H.M. : (1) Potential energy is always equal to its K.E. (2) Average potential and kinetic energy over any given time interval are always equal. (3) Sum of the kinetic and potential energy at any point of time is…2021 · 31 Aug · Shift 2 · Q60 · MCQ
The displacement time graph of a particle executing S.H.M is given in figure : (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at t = $\frac{3 T}{4}$ (B) The… Includes diagram2020 · 2 Sep · Shift 2 · Q54 · MCQ
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the…2020 · 3 Sep · Shift 2 · Q63 · MCQ
When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t) = y0 sin2 $ω$ t, where 'y' is measured from the lower end of unstretched spring. Then $ω$ is:2020 · 6 Sep · Shift 2 · Q40 · MCQ
A simple pendulum is being used to determine th value of gravitational acceleration g at a certain place. Th length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50 s. The…2020 · 8 Jan · Shift 2 · Q50 · MCQ
A spring mass system (mass m, spring constant k and natural length $l$ ) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about…2020 · 9 Jan · Shift 2 · Q64 · MCQ
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by…2019 · 9 Jan · Shift 2 · Q57 · MCQ
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :2019 · 9 Jan · Shift 2 · Q63 · MCQ
A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds…2019 · 10 Jan · Shift 2 · Q57 · MCQ
A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $ω$ …2019 · 10 Jan · Shift 2 · Q60 · MCQ
A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin $\frac{π t}{90}$ . The ratio of kinetic to potential energy of this particle at t = 210 s will be:2019 · 11 Jan · Shift 1 · Q70 · MCQ
A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy…2019 · 11 Jan · Shift 2 · Q49 · MCQ
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be :2019 · 11 Jan · Shift 2 · Q61 · MCQ
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length $ℓ$ and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The… Includes diagram2019 · 12 Jan · Shift 1 · Q70 · MCQ
A simple harmonic motion is represented by : y = 5 (sin 3 $π$ t + $3$ cos 3 $π$ t) cm The amplitude and time period of the motion are :2019 · 12 Jan · Shift 2 · Q63 · MCQ
Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures. x(t) = A sin (at + $δ$ ) y(t) = B sin (bt) Identify the correct match below.2018 · 15 Apr · Shift 2 · Q61 · MCQ
A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The freqquency of the oscillation is :2018 · 16 Apr · Shift 1 · Q61 · MCQ
An oscillator of mass M is at rest in its equilibrium position in a potential V = $\frac{1}{2}$ k(x $-$ X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process…2018 · 16 Apr · Shift 1 · Q63 · MCQ
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02…2018 · Shift 0 · Q55 · MCQ
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1 . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is $\frac{π}{4}$ .2017 · 8 Apr · Shift 1 · Q63 · MCQ
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of…2017 · 8 Apr · Shift 1 · Q68 · MCQ
A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:2017 · Shift 0 · Q44 · MCQ
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and I, respectively. At time t = 0 one particle has…2016 · 9 Apr · Shift 1 · Q61 · MCQ
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer…2016 · 10 Apr · Shift 1 · Q56 · MCQ
A particle performs simple harmonic motion with amplitude $A .$ Its speed is trebled at the instant that it is at a distance $\frac{2 A}{3}$ from equilibrium position. The new amplitude of the motion is:2016 · Shift 0 · Q54 · MCQ
For a simple pendulum, a graph is plotted between its kinetic energy $(K E)$ and potential energy $(P E)$ against its displacement $d .$ Which one of the following represents these correctly? $(g r a p h s a r esc h e ma t i c an d n o t d r a w n t osc a l e)$ 2015 · Shift 0 · Q59 · MCQ
A pendulum made of a uniform wire of cross sectional area $A$ has time period $T .$ When an additional mass $M$ is added to its bob, the time period changes to $T_{M .}$ If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ …2015 · Shift 0 · Q60 · MCQ
The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution.…2015 · Shift 0 · Q69 · MCQ
A particle moves with simple harmonic motion in a straight line. In first $τ s,$ after starting from rest it travels a distance $a,$ and in next $τ s$ it travels $2 a,$ in same direction, then:2014 · Shift 0 · Q62 · MCQ
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M .$ The piston and the cylinder have equal cross sectional area $A$ . When the piston is in equilibrium, the volume of the gas is $V_{0}$ and…2013 · Shift 0 · Q67 · MCQ
Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $ω$ along the $x$ -axis. Their mean position is separated by distance $X_{0} (X_{0} > A)$ . If the maximum separation between…2011 · Shift 0 · Q65 · MCQ
A mass $M,$ attached to a horizontal spring, executes $S . H . M .$ with amplitude $A_{1} .$ When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2} .$ The…2011 · Shift 0 · Q67 · MCQ
If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?2009 · Shift 0 · Q65 · MCQ
The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 1 0^{- 2} cos π t$ metre. The time at which the maximum speed first occurs is2007 · Shift 0 · Q86 · MCQ
A point mass oscillates along the $x$ -axis according to the law $x = x_{0} cos (ω t - π /4) .$ If the acceleration of the particle is written as $a = A cos (ω t + δ),$ then2007 · Shift 0 · Q87 · MCQ
Two springs, of force constant $k_{1}$ and $k_{2}$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f .$ If both $k_{1}$ and $k_{2}$ are made four times their original values, the frequency of oscillation… Includes diagram2007 · Shift 0 · Q88 · MCQ
A particle of mass $m$ executes simple harmonic motion with amplitude a and frequency $v .$ The average kinetic energy during its motion from the position of equilibrium to the end is2007 · Shift 0 · Q89 · MCQ
Starting from the origin a body oscillates simple harmonically with a period of $2 s .$ After what time will its kinetic energy be $75%$ of the total energy?2006 · Shift 0 · Q111 · MCQ
The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7 mm,$ is $4.4 m / s .$ The period of oscillation is2006 · Shift 0 · Q112 · MCQ
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $ω .$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time2006 · Shift 0 · Q125 · MCQ
Two simple harmonic motions are represented by the equations $y_{1} = 0.1 sin (100 π t + \frac{π}{3})$ and $y_{2} = 0.1 cos π t .$ The phase difference of the velocity of particle $1$ with respect to the velocity…2005 · Shift 0 · Q142 · MCQ
The function $sin^{2} (ω t)$ represents2005 · Shift 0 · Q155 · MCQ
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would2005 · Shift 0 · Q156 · MCQ
If a simple harmonic motion is represented by $\frac{d ^{2} x}{d t ^{2}} + α x = 0.$ its time period is2005 · Shift 0 · Q157 · MCQ
The bob of a simple pendulum executes simple harmonic motion in water with a period $t,$ while the period of oscillation of the bob is $t_{0}$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3) \times 1000 k g / m^{3} .$ …2004 · Shift 0 · Q176 · MCQ
A particle at the end of a spring executes $S . H . M$ with a period $t_{1}$ . While the corresponding period for another spring is $t_{2}$ . If the period of oscillation with the two springs in series is $T$ then2004 · Shift 0 · Q177 · MCQ
The total energy of particle, executing simple harmonic motion is2004 · Shift 0 · Q178 · MCQ
A particle of mass $m$ is attached to a spring (of spring constant $k$ ) and has a natural angular frequency $ω_{0} .$ An external force $F (t)$ proportional to $cos ω t (ω e ω_{0})$ is applied to the…2004 · Shift 0 · Q179 · MCQ
A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S H M$ of time period $T .$ If the mass is increased by $m .$ the time period becomes $\frac{5 T}{3}$ . Then…2003 · Shift 0 · Q158 · MCQ
Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring of spring constant $k_{1}$ and $k_{2}$ , respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ …2003 · Shift 0 · Q159 · MCQ
The length of a simple pendulum executing simple harmonic motion is increased by $21%$ . The percentage increase in the time period of the pendulum of increased length is2003 · Shift 0 · Q160 · MCQ
A body executes simple harmonic motion. The potential energy $(P . E),$ the kinetic energy $(K . E)$ and total energy $(T . E)$ are measured as a function of displacement $x .$ Which of the following statements is true ?2003 · Shift 0 · Q161 · MCQ
The displacement of particle varies according to the relation $x = 4$ $(cos π t + sin π t) .$ The amplitude of the particle is2003 · Shift 0 · Q162 · MCQ
If a spring has time period $T,$ and is cut into $n$ equal parts, then the time period of each part will be2002 · Shift 0 · Q153 · MCQ
In a simple harmonic oscillator, at the mean position2002 · Shift 0 · Q154 · MCQ
A child swinging on a swing in sitting position, stands up, then the time period of the swing will2002 · Shift 0 · Q155 · MCQ