If the time period of a two meter long simple pendulum is $2\, s$, the acceleration due to gravity at the place where pendulum is executing $S.H.M.$ is

Time period of a simple pendulum will be double, if we

The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$

The displacement $y(t) = A\,\sin \,(\omega t + \phi )$ of a pendulum for $\phi = \frac {2\pi }{3}$ is correctly represented by

Two simple pendulums of lengths $1.44 \,m$ and $1\, m$ start swinging together. After how many vibrations will they again start swinging together