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

For the minimum time period condition,find the average potential energy between $t = 0$ to $t = 0.05 \ s$ (take $g = 10 \ m/s^2$).

At which point (place) does a particle executing $SHM$ have maximum kinetic energy and maximum potential energy?

$A$ block kept on a frictionless horizontal surface is connected to one end of a horizontal spring of constant $100 \text{ Nm}^{-1}$ whose other end is fixed to a rigid vertical wall. Initially, the block is at its equilibrium position. The block is pulled to a distance of $8 \text{ cm}$ and released. The kinetic energy of the block when it is at a distance of $3 \text{ cm}$ from the mean position is (in $\text{ J}$)

There is a body having mass $m$ and performing $SHM$ with amplitude '$a$'. There is a restoring force $F = -Kx$, where $x$ is the displacement. The total energy of the body depends upon which of the following?

$A$ 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 $s$)?