$A$ 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:

The amplitude of a simple pendulum is $10 \ cm$. When the pendulum is at a displacement of $4 \ cm$ from the mean position,the ratio of kinetic and potential energies at that point is

$A$ simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position,the frequency of its oscillations will be

$A$ simple pendulum oscillating in air has period $T.$ The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$ of the material of the bob. If the bob is inside the liquid all the time,its period of oscillation in this liquid is:

The length of a simple pendulum is $l$ and its maximum angular displacement is $\theta$. What is its maximum kinetic energy $(K.E.)$?

The time period of a simple pendulum of length $L$ as measured in an elevator descending with acceleration $\frac{g}{3}$ is