When the displacement of a simple harmonic oscillator is one third of its amplitude,the ratio of total energy to the kinetic energy is $\frac{x}{8}$,where $x=$ . . . . . . .

The kinetic energy of a particle executing simple harmonic motion in a straight line is $pv^2$ and the potential energy is $qx^2$,where $v$ is the speed at a distance $x$ from the mean position. Its time period is given by the expression:

The variations of kinetic energy $K(x)$,potential energy $U(x)$,and total energy $E$ as a function of displacement $x$ of a particle in $SHM$ are as shown in the figure. The value of $|x_0|$ is

$A$ body of mass $1\,kg$ is executing simple harmonic motion. Its displacement $y$ (in $cm$) at $t$ seconds is given by $y = 6\sin(100t + \pi/4)$. Its maximum kinetic energy is ..... $J$.

For a particle executing simple harmonic motion, the kinetic energy of the particle at a distance of $4 \,cm$ from the mean position is $\frac{1}{3}$ of the maximum kinetic energy. The amplitude of the motion is

$A$ 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