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 $J$)

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

The graph shows the variation of displacement of a particle executing $S$.$H$.$M$. with time. We infer from this graph that

$A$ particle starts from the mean position and performs $S.H.M.$ with a period of $4 \ s$. At what time is its kinetic energy $50 \%$ of its total energy (in $s$)?

For a particle executing simple harmonic motion,the kinetic energy $K$ is given by $K = K_0 \cos^2 \omega t$. The maximum value of potential energy is

An object of mass $3 \,kg$ is executing simple harmonic motion with an amplitude $\frac{2}{\pi} \,m$. If the kinetic energy of the object when it crosses the mean position is $6 \,J$, the time period of oscillation of the object is (in $\,s$)