Out of the following functions representing motion of a particle which represents SHM I. $y=\sin \omega…
Out of the following functions representing motion of a particle which represents SHM
I. $y=\sin \omega t-\cos \omega t$
II. $y=\sin ^3 \omega t$
III. $y=5 \cos \left(\frac{3 \pi}{4}-3 \omega t\right)$
IV. $y=1+\omega t+\omega^2 t^2$
Only (IV) does not represent SHM
(I) and (III)
(I) and (II)
Only (I)
Solution
For a simple harmonic motion
$\frac{d^2 y}{d t^2} \propto-y$
Hence, equation $y=\sin \omega t-\cos \omega t$ and $y=5 \cos \left(\frac{3 \pi}{4}-3 \omega t\right)$ are satisfying this condition and equation $y=1+\omega t+\omega^2 t^2$ is not periodic and $y=\sin ^3 \omega t$ is periodic but not SHM.
Option (3) is correct
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