Two pendulums differ in lengths by $22 \ cm$. They oscillate at the same place such that one of them makes $15 \ oscillations$ and the other makes $18 \ oscillations$ during the same time. The lengths (in $cm$) of the pendulums are

$A$ 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 $60^\circ$?

The bob of a pendulum of mass $m$, suspended by an inextensible string of length $L$ as shown in the figure, carries a small charge $q$. An infinite horizontal plane conductor with uniform surface charge density $\sigma$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise,then the loss in time of the clock per day is ........... $s$.

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom,the period of oscillation will

$A$ simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is