The path length of oscillation of a simple pendulum of length $1 \,m$ is $16 \,cm$. Its maximum velocity is (Take $g = \pi^2 \,m/s^2$).

The time period of a simple pendulum when it is made to oscillate on the surface of the moon:

$A$ simple pendulum with a bob of mass $m$ and length $x$ is held in position at an angle $\theta_1$ and then at an angle $\theta_2$ with the vertical. When released from these positions,the speeds with which it passes the lowest position are $v_1$ and $v_2$ respectively. Then,the ratio $\frac{v_1}{v_2}$ is .............

$A$ disc of mass $m$ and radius $R$ is attached to the ceiling with the help of two ropes of length $l$. Find the time period of small oscillations of the disc in the plane of the disc.

$A$ simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is $4$ times the minimum tension,then the value of $\theta$ is

$A$ bob of mass $m$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $1/4$ times that of the bob and the length of the thread is increased by $1/3$ of the original length,then the time period of the simple harmonic oscillations will be :-