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

$A$ second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$,where $R$ is the radius of the earth. The time period of the pendulum is

$A$ 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:

Two pendulums have time periods $T$ and $\frac{5T}{4}$. They start $S.H.M.$ at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation (in $^o$)?

Which of the following plots represents schematically the dependence of the time period of a pendulum,if measured and plotted as a function of the amplitude of its oscillations? (Note: amplitude need not be small)

$A$ pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point,the string is cut. Which trajectory is possible for the bob afterwards?