The kinetic energy and the potential energy of a particle executing $S.H.M.$ are equal. The ratio of its displacement and amplitude will be

As a body performs $S.H.M.$,its potential energy $U$ varies with time $t$ as indicated in:

$A$ 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 $\text{ J}$)

$A$ linear harmonic oscillator of force constant $2 \times 10^6\,N/m$ and amplitude $0.01\,m$ has a total mechanical energy of $160\,J$. Which of the following statements is correct?

The displacement of a particle in simple harmonic motion $(SHM)$ is given by $y = \sqrt{3 \pi} \sin \left(\frac{100}{\pi} t + \frac{\pi}{4}\right)$. What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?

The average energy possessed by an oscillator at a temperature $300 \ K$ is (Boltzmann constant $= 1.38 \times 10^{-23} \ J K^{-1}$).