$A$ particle of mass $m$ oscillates with simple harmonic motion between points $x_1$ and $x_2$,the equilibrium position being $O$. Its potential energy is plotted. It will be as given below in the graph:

For a particle executing $S.H.M.$, its potential energy is $8$ times its kinetic energy at a certain displacement '$x$' from the mean position. If '$A$' is the amplitude of $S.H.M.$, the value of '$x$' is

$A$ particle starts from mean position and performs $S.H.M.$ with period $T = 6 \text{ s}$. At what time is its kinetic energy $50\%$ of its total energy (in $\text{ s}$)? (Given: $\cos 45^\circ = 1/\sqrt{2}$)

The total mechanical energy of a particle executing simple harmonic motion is $E$. When the displacement is half the amplitude,its kinetic energy will be

An object of mass $0.2 \,kg$ executes simple harmonic motion along the $x$-axis with a frequency of $(\frac{25}{\pi}) \,Hz$. At the position $x=0.04 \,m$, the object has a kinetic energy of $0.5 \,J$ and a potential energy of $0.4 \,J$. The amplitude of oscillation is ............ $cm$.

$A$ body is executing simple harmonic motion. At a displacement $x$,its potential energy is $E_1$ and at a displacement $y$,its potential energy is $E_2$. The potential energy $E$ at a displacement $(x + y)$ is