The displacement between the position of maximum potential energy and the position of maximum kinetic energy for a particle executing $S.H.M.$ is

The displacement-time graph of a particle executing $SHM$ is as shown in the figure. The corresponding graph between potential energy $(PE)$ and time is:

The mass of a particle is $1 \ kg$ and it is moving along the $x$-axis. The period of its oscillation is $\frac{\pi}{2} \ s$. Its potential energy at a displacement of $0.2 \ m$ is (in $J$)

$A$ particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches a distance of $4 \,cm$ from the mean position,it is stopped for a moment and then released. The new energy of vibration will be ........... $J$.

As a body performs $S.H.M.$,its potential energy $U$ varies with time $t$ as indicated in:

The maximum restoring force of a body executing $SHM$ is $\alpha$ and the total energy is $\beta$. Obtain its amplitude in terms of $\beta$ and $\alpha$.