$A$ pendulum is oscillating at a frequency of $8 \,Hz$. Suddenly, the string of the pendulum is clamped at its midpoint. What is the new frequency of oscillations (in $\,Hz$)?

The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and the time period of oscillations to be $2.0 \, s$,the tension in the string when the bob passes through $O$ is

For a simple pendulum,the graph between $L$ and $T$ will be:

If the length of a simple pendulum is increased by $300\%$,then the time period will be increased by ..... $\%$

$A$ light balloon filled with helium of density $\rho_{He}$ is tied to a long light string of length $l$ and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released,then:

$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$