The time period of a simple pendulum of length $L$ as measured in an elevator descending with acceleration $\frac{g}{3}$ is

$A$ simple pendulum of length $L$ has mass $m$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is ($g =$ acceleration due to gravity).

$A$ simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in a horizontal position from the wall and is left free to move. The bob hits the wall,and the coefficient of restitution is $\frac{2}{\sqrt{5}}$. After how many collisions will the amplitude of vibration become less than $60^\circ$?

An oscillating pendulum suspended from the roof of a lift which is at rest has time period $T_1$. When the lift moves up with acceleration $a$, its time period is $T_2$. When the lift moves down with acceleration $a$, its time period is $T_3$. The relation between $T_1$, $T_2$, and $T_3$ is:

$A$ simple pendulum executing $S.H.M.$ is falling freely along with its support. Then:

$A$ plate oscillates with a time period $T$. If another plate is suddenly placed on the first plate,what happens to the time period?