The distance covered by a particle undergoing $SHM$ in one time period is (amplitude $= A$).

Match the following functions with their corresponding nature of motion, where $\omega$ is a constant:

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 $SHM$ $(T = 2\pi/\omega)$

$A$ point particle of mass $0.1\, kg$ is executing $S.H.M.$ with an amplitude of $0.1\, m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \, J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^o$.

$A$ particle moves on the $x-$axis according to the equation $x = x_0 \sin^2 \omega t$. Is the motion simple harmonic?

Identify the correct definition.

$A$ $S.H.M.$ is represented by $x = 5\sqrt{2} (\sin 2\pi t + \cos 2\pi t).$ The amplitude of the $S.H.M.$ is .... $cm$.