The maximum potential energy of a block executing $S.H.M.$ is $E$ and amplitude of oscillation is $A$. The kinetic energy of the block at amplitude $A/2$ is

The equation of motion of a particle executing simple harmonic motion is given by $x=3 \sin \left(6 t+\frac{\pi}{6}\right)$,where $x$ is in metres and $t$ is in seconds. The ratio of the potential and kinetic energies of the particle at time $t=0$ is

$A$ particle of mass $4 \,kg$ is executing $SHM$. Its displacement is given by the equation $y=8 \cos [100 t+\pi / 4] \,cm$. Its maximum kinetic energy is (in $\,J$)

$A$ body is performing $S.H.M.$ of amplitude $A$. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum,is

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:

$A$ body is executing $S.H.M$. At a displacement $x$ its potential energy is $9 \ J$ and at a displacement $y$ its potential energy is $16 \ J$. The potential energy at displacement $(x+y)$ is (in $J$)