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(C) function represents $SHM$ if it can be expressed in the form $y = A \sin(\omega t + \phi)$ or $y = A \cos(\omega t + \phi)$.For $(A): y = \sin \om

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only $(A)$ and $(C)$

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(C) function represents $SHM$ if it can be expressed in the form $y = A \sin(\omega t + \phi)$ or $y = A \cos(\omega t + \phi)$.For $(A): y = \sin \omega t - \cos \omega t = \sqrt{2} \left[ \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t \right] = \sqrt{2} \sin \left( \omega t - \frac{\pi}{4} \right)$. This is a $SHM$.For $(B): y = \sin^3 \omega t = \frac{1}{4} [3 \sin \omega t - \sin 3 \omega t]$. This is a superposition of two $SHMs$ with different frequencies,so it is periodic but not $SHM$.For $(C): y = 5 \cos \left( \frac{3\pi}{4} - 3\omega t \right) = 5 \cos \left( 3\omega t - \frac{3\pi}{4} \right)$. This is a $SHM$ with angular frequency $3\omega$.For $(D): y = 1 + \omega t + \omega^2 t^2$. This is a quadratic function of time,representing non-periodic motion.Thus,both $(A)$ and $(C)$ represent $SHM$.

Out of the following functions representing the motion of a particle,which represent $SHM$?
$(A)\; y = \sin \omega t - \cos \omega t$
$(B)\; y = \sin^3 \omega t$
$(C)\; y = 5 \cos \left( \frac{3\pi}{4} - 3\omega t \right)$
$(D)\; y = 1 + \omega t + \omega^2 t^2$

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Out of the following functions representing the motion of a particle,which represent $SHM$?$(A)\; y = \sin \omega t - \cos \omega t$$(B)\; y = \sin^3 \omega t$$(C)\; y = 5 \cos \left( \frac{3\pi}{4} - 3\omega t \right)$$(D)\; y = 1 + \omega t + \omega^2 t^2$