What is the velocity of the bob of a simple pendulum at its mean position,if it is able to rise to a vertical height of $10 \, cm$ ......... $m/s$? (Take $g = 9.8 \, m/s^2$)

$A$ cylindrical plastic bottle of negligible mass is filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released,it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5\, cm$,then $\omega$ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$).

The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio:

Let $l_1$ be the length of a simple pendulum. Its length changes to $l_2$ to increase the periodic time by $20 \%$. The ratio $\frac{l_2}{l_1}$ is:

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?

$A$ simple pendulum is vibrating in an evacuated chamber. It will oscillate with