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(D) simple harmonic motion $(SHM)$ is defined by an equation of the form $x(t) = A\sin(\omega t + \phi)$ or $x(t) = A\cos(\omega t + \phi)$.Option $A$

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(D) simple harmonic motion $(SHM)$ is defined by an equation of the form $x(t) = A\sin(\omega t + \phi)$ or $x(t) = A\cos(\omega t + \phi)$.Option $A$ is $x = A\sin(\omega t + \delta)$,which is a standard $SHM$ equation.Option $B$ is $x = B\cos(\omega t + \phi)$,which is also a standard $SHM$ equation.Option $C$ is $x = A\sin \omega t \cos \omega t$. Using the trigonometric identity $\sin(2	heta) = 2\sin	heta \cos	heta$,we can rewrite this as $x = \frac{A}{2}\sin(2\omega t)$. This represents an $SHM$ with amplitude $\frac{A}{2}$ and angular frequency $2\omega$.Since all three expressions represent simple harmonic motion,the correct answer is $D$.

List-$I$	List-$II$
$A$. $\sin^2 \omega t$	$I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
$B$. $\sin^3 \omega t$	$II$. Periodic but not $SHM$ $(T = \pi/\omega)$
$C$. $\sin \omega t + \cos \pi \omega t$	$III$. Non-periodic
$D$. $\cos \omega t + \cos 2\omega t$	$IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$

Which of the following expressions represent simple harmonic motion?

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