The motion of a simple pendulum executing $S.H.M.$ is represented by the following equation:
$Y = A \sin (\pi t + \phi)$,where time is measured in $seconds$.
The length of the pendulum is .............$cm$.

The graph between the time period $(T)$ and the length $(l)$ of a simple pendulum is

$A$ simple pendulum,suspended from the ceiling of a lift,has a period of oscillation $T$,when the lift is at rest. If the lift starts moving upwards with an acceleration $a = 3g$,then the new period will be

$A$ simple pendulum is suspended in a lift which is going up with an acceleration $5 \ m/s^2$. An electric field of magnitude $5 \ N/C$ and directed vertically upward is also present in the lift. The charge of the bob is $1 \ mC$ and mass is $1 \ mg$. Taking $g = \pi^2 \ m/s^2$ and length of the simple pendulum $1 \ m$,the time period of the simple pendulum is ...... $s$.

$A$ 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 ..... $\%$

$A$ simple pendulum of mass $200\, g$ and length $100\, cm$ is moved aside until the string makes an angle of $60^\circ$ with the vertical. The kinetic and potential energies of the bob,when the string is inclined at $30^\circ$ to the vertical,are