$A$ particle executing simple harmonic motion of amplitude $5\, cm$ has a maximum speed of $31.4\, cm/s$. The frequency of its oscillation is ..... $Hz$.

Select the wrong statement about simple harmonic motion $(S.H.M.)$.

The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...

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

Study of which motion is required to understand many physical phenomena?

Identify the correct definition.