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

The mass of a particle is 1 kg and it is moving along $X$-axis. The period of its oscillation is $\frac{\pi}{2}$. Its potential energy at a displacement of 0.2 m is

The potential energy of a particle of mass 10 g as a function of displacement $x$ is $\left(50 x^2+100\right) \mathrm{J}$. The frequency of oscillation is

A horizontal board is performing simple harmonic oscillations horizontally with an amplitude 0.3 m and a period of 4 s . The minimum coefficient of friction between a heavy body placed on the board if the body does not slip will be