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Oscillations question

2014 · Q157
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Oscillations question

2014 · Q157

NEETPhysicsOscillationsMCQ+4 / −1
The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos(ωt)\left( {\omega t} \right)(ωt)
where X = displacement at time t
ω\omegaω = frequency of oscillation
Which one of the following graphs shows correctly the variation a with t?
Here a = acceleration at time t
T = time period
  1. A
    AIPMT 2014 Physics - Oscillations Question 46 English Option 1
  2. B
    AIPMT 2014 Physics - Oscillations Question 46 English Option 2
  3. C
    AIPMT 2014 Physics - Oscillations Question 46 English Option 3
  4. D
    AIPMT 2014 Physics - Oscillations Question 46 English Option 4
View written solutionFree

Correct answer: C

Here, X = Acosω\omega ωt

∴\therefore∴ Velocity, v=dXdt=ddt(Acos⁡ωt)v = {{dX} \over {dt}} = {d \over {dt}}\left( {A\cos \omega t} \right)v=dtdX​=dtd​(Acosωt)

=−Aωsin⁡ωt = - A\omega \sin \omega t=−Aωsinωt

Acceleration, a=dvdt=ddt(−Aωsin⁡ωt)a = {{dv} \over {dt}} = {d \over {dt}}\left( { - A\omega \sin \omega t} \right)a=dtdv​=dtd​(−Aωsinωt)

=−Aω2cos⁡ωt = - A{\omega ^2}\cos \omega t=−Aω2cosωt

Hence the variation of a with t is correctly shown by graph (c).

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