The P.E. of an oscillating particle at the rest position is $15\mathrm{J}$ and its average K.E. is $5\mathrm{J}$. The total energy of the particle at any instant will be: 

Block $A$ in the figure is released from the rest when the extension in the spring is $x_0$. The maximum downward displacement of the block.

A system is shown in the figure. The time period for small oscillations of the two blocks will be:

A block of mass $0.9\mathrm{kg}$ attached to a spring of force constant $\mathrm{K}$ is compressed by $\sqrt{2} \mathrm{cm}$ and the block is at a distance $\frac{1}{\sqrt{2}}\mathrm{cm}$ from the wall. When the block is released, it makes elastic collision with the wall and its period of motion is $0.2\mathrm{s}$. The value of $K$ is (take ${\pi }^2=10$)

A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. A small peg is placed a distance $2\mathrm{L}/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?