$A$ horizontal platform with an object placed on it is executing $S.H.M.$ in the vertical direction. The amplitude of oscillation is $3.92 \times 10^{-3} \, m$. What must be the least period of these oscillations,so that the object is not detached from the platform (in $, s$)?

$A$ particle is executing $SHM$ with an amplitude $A$ and angular frequency $\omega$. The ratio of the maximum acceleration to the maximum velocity of the particle is:

Determine whether the following statements are True or False:
$1.$ The acceleration of $SHO$ at the mean position is maximum.
$2.$ The mechanical energy of $SHO$ depends on the maximum displacement.
$3.$ The periodic time for a seconds pendulum is $1 \, s$.
$4.$ If the frequency of $SHM$ is $v$,then the frequency of kinetic energy is also $v$.

The maximum velocity and maximum acceleration of a particle performing a linear $S.H.M.$ are $\alpha$ and $\beta$ respectively. Then the path length of the particle is

When a body is in $S.H.M.$,match the following:

List-$I$	List-$II$
$A$. Velocity is maximum	$I$. Acceleration is maximum
$B$. $K.E.$ is $\left(\frac{3}{4}\right)^{\text{th}}$ of total energy	$II$. At mean position
$C$. $P.E.$ is $\left(\frac{3}{4}\right)^{\text{th}}$ of total energy	$III$. At half of the amplitude
$D$. Acceleration is maximum	$IV$. At $\frac{\sqrt{3}}{2}$ times the amplitude

$A$ block is placed on a horizontal plank. The plank is performing $SHM$ along a vertical line with an amplitude of $40 \, cm$. The block just loses contact with the plank when the plank is momentarily at rest. Then: