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

A test tube of mass 6 g and uniform area of cross-section $10 \mathrm{~cm}^2$ is floating in water vertically when 10 g of mercury is in the bottom. The tube is depressed by a small amount and then released. The time period of oscillation is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A 3 kg block is connected as shown in the figure. Spring constants of two springs $k_1$ and $k_2$ are $50 \mathrm{Nm}^{-1}$ and $150 \mathrm{Nm}^{-1}$ respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $\left(g=10 \mathrm{~ms}^{-2}\right)$