$A$ 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 $\,m$)

When a pendulum clock is running fast,what should be done to adjust it to the true time?

What is a simple pendulum? Deduce an expression for the time period of a simple pendulum.

$A$ 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 has a time period $T_1$. The point of suspension is now moved upward according to the equation $y = kt^2$,where $k = 1 \ m/s^2$. If the new time period is $T_2$,then the ratio $\frac{T_1^2}{T_2^2}$ will be (take $g = 10 \ m/s^2$):

Two pendulums having lengths $1.0 \ m$ and $1.21 \ m$ start oscillating simultaneously in the same phase. They will again come in the same phase after how many oscillations of the smaller pendulum?