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Oscillations question

2015 · Q114
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Oscillations question

2015 · Q114

NEETPhysicsOscillationsMCQ+4 / −1
When two displacements represented by y1 = a sin(ωt){\left( {\omega t} \right)}(ωt) and y2 = b cos(ωt){\left( {\omega t} \right)}(ωt) aresuperimposed the motion is
  1. A
    simple harmonic with amplitude a2+b2\sqrt {{a^2} + {b^2}}a2+b2​
  2. B
    simple harmonic with amplitude (a+b)2{{\left( {a + b} \right)} \over 2}2(a+b)​
  3. C
    not a simple harmonic
  4. D
    simple harmonic with amplitude ab{a \over b}ba​
View written solutionFree

Correct answer: A

Here, y1=asin⁡ωt{y_1} = a\sin \omega ty1​=asinωt

y2=bcos⁡ω=bsin⁡(ωt+π2){y_2} = b\cos \omega = b\sin \left( {\omega t + {\pi \over 2}} \right)y2​=bcosω=bsin(ωt+2π​)

AIPMT 2015 Cancelled Paper Physics - Oscillations Question 47 English Explanation

Hence, resultant motion is SHM with amplitude a2+b2\sqrt {{a^2} + {b^2}} a2+b2​.

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