Two pendulums of length $1.21 \,m$ and $1.0 \,m$ start vibrating. At some instant,the two are in the mean position in the same phase. After how many vibrations of the longer pendulum will the two be in phase again?

$A$ uniform rod of length $1.8 \,m$ suspended by an end is made to undergo small oscillations. Find the length of the simple pendulum having the mass and time period equal to that of the rod. (in $\,m$)

$A$ pendulum suspended from the ceiling of a train has a period $T$,when the train is at rest. When the train is accelerating with a uniform acceleration $a$,the period of oscillation will

The time period of a simple pendulum will be doubled if we:

$A$ 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 of time period $1\,s$ and length $l$ is hung from a fixed support at $O$. The bob is at a distance $H$ vertically above $A$ on the ground. The amplitude is $\theta_0$. The string snaps at $\theta = \frac{\theta_0}{2}$. Find the time taken by the bob to hit the ground and the distance from $A$ where the bob hits the ground. Assume $\theta_0$ to be small,so that $\sin \theta_0 \approx \theta_0$ and $\cos \theta_0 \approx 1$.