A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation  $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.

How many amplitudes of $SHO$ covers the distance in the half period ?

A pendulum bob has a speed of $3\, {m} / {s}$ at its lowest position. The pendulum is $50 \,{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $ .......\,{m} / {s}$ $\left(g=10 \,{m} / {s}^{2}\right)$

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$.The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true

A hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be