Amplitude of a $SHO$ is $\sqrt{5} \ cm$. At what displacement from the mean position the ratio of kinetic energy to potential energy is $4$ (in $cm$)?

$A$ particle is vibrating simple harmonically with an amplitude $a$. The displacement of the particle when its energy is half kinetic and half potential is

$A$ particle is executing $S.H.M.$ with time period $T^{\prime}$. If the time period of its total mechanical energy is $T$,then $\frac{T^{\prime}}{T}$ is ........

$A$ particle of mass $m$ is hanging vertically by an ideal spring of force constant $K$. If the mass is made to oscillate vertically,its total energy is

The position of a particle executing simple harmonic motion is given by $x(t) = 2 \cos \left(\frac{\pi}{15} t - \frac{\pi}{2}\right)$, where $x$ is in centimetre and $t$ is in seconds. The time period of the kinetic energy of the particle in seconds is

The total energy of a particle performing $S.H.M.$ depends on: