$A$ child swinging on a swing in a sitting position stands up. What will happen to the time period of the swing?

$A$ simple pendulum of length $l$ and having a bob of mass $M$ is suspended in a car. The car is moving on a circular track of radius $R$ with a uniform speed $v$. If the pendulum makes small oscillations in a radial direction about its equilibrium position,what will be its time period?

$A$ trolley of mass $m_1$ is placed on a horizontal rigid pair of rails at the same height. $A$ mass $m_2$ is suspended from the trolley vertically by means of an ideal massless rope. The rope hangs between the rails without touching them. The trolley can move along smooth rails but cannot move in any other direction. The suspended mass is given a small oscillation and performs $SHM$ after being displaced slightly from its stable equilibrium position in two ways: first,perpendicular to the rails,and second,parallel to the rails. The ratio of the time periods of these two $SHM$s (second case to first case) is:

In $S.H.M.$,a simple pendulum oscillates with frequency $f$. If the length of the pendulum is increased by three times its original length,then the frequency of oscillation of the pendulum will be

The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and the time period of oscillations to be $2.0 \, s$,the tension in the string when the bob passes through $O$ is

$A$ simple pendulum of length $l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of the same size,having a density $x$ times that of brass,replaces the brass bob and its length is changed so that the period becomes $2T$,then the new length is: