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

If a simple pendulum is taken to a place where $g$ decreases by $2\%$,then the time period:

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

$A$ 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 $\,Hz$)?

$A$ pendulum is swinging in an elevator. Its period will be greatest when the elevator is

$A$ $50 \ cm$ long simple pendulum is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3} \ g \ m/s^2$. The time period of small oscillations of the pendulum about its equilibrium position is $.... \ s$ $\left(g=\pi^2 \ m/s^2\right):-$