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Q.

Which of the following functions represents a simple harmonic oscillation?

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a

$large sin omega t - cos omega t$

b

(2t²-3t)

c

$large {sin ^3}omega t + sin 2omega t$

d

$large sin omega t - sin 2omega t$

answer is A.

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Detailed Solution

$large y, = ,sin omega t - Bcos omega t......(a)$

$large y, = ,sqrt 2 ,sin left( {omega t - frac{pi }{4}} right)......(b)$

This equation is a periodic function with a time period $large frac{{2pi }}{omega }$ and amplitude $large sqrt 2$ . Also equation - (a) represents the super position of two SHM's of same frequency. So the resulting motion is another SHM of same frequency.

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Which of the following functions represents a simple harmonic oscillation?