A simple pendulum starts oscillating simple harmonically from its mean position ( $\mathrm{x}=0$ ) with amplitude ' $a$ ' and periodic time ' $T$ '. The magnitude of velocity of pendulum at $x=\frac{a}{2}$ is

A simple pendulum is suspended from ceiling of a lift when lift is at rest its period is ' T '. With what acceleration ' $a$ ' should lift be accelerated upward in order to reduce the period to ' $T$ '? (take ' g ' as acceleration due to gravity)

A particle is performing S.H.M. starting from extreme position. Graphical representation shows that between displacement and acceleration, there is a phase difference of

A mass ' $M$ ' attached to a horizontal spring executes S.H.M. of amplitude $A_1$. When the mass M passes through its mean position, then a smaller mass ' $m$ ' is placed over it and both of them move together with amplitude $\mathrm{A}_2$. The ratio $\left(\frac{A_1}{A_2}\right)$ is