A piece of wood has length, breadth and height, ' $a$ ', ' $b$ ' and ' $c$ ' respectively. Its relative density, is ' $d$ '. It is floating in water such that the side ' $a$ ' is vertical. It is pushed down a little and released. The time period of S.H.M. executed by it is ($\mathrm{g}=$ acceleration due to gravity)

All the springs in fig. (a), (b) and (c) are identical, each having force constant K . Mass attached to each system is ' $m$ '. If $T_a, T_b$ and $T_c$ are the time periods of oscillations of the three systems respectively, then

A simple pendulum of length ' $L$ ' has mass ' $M$ ' and it oscillates freely with amplitude ' $A$ '. At extreme position, its potential energy is

A particle performing S.H.M. starts from equilibrium position and its time period is 12 second. After 2 seconds its velocity is $\pi \mathrm{m} / \mathrm{s}$. Amplitude of the oscillation is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0 \cdot 5, \sin 60^{\circ}=\cos 30^{\circ}=\sqrt{3} / 2\right]$