$A$ simple pendulum of length $L$ has mass $m$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is (where $g$ is the acceleration due to gravity):

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

Identify the correct statement.

The angular velocity and the amplitude of a simple pendulum are $\omega$ and $a$ respectively. At a displacement $X$ from the mean position,if its kinetic energy is $T$ and potential energy is $V$,then the ratio of $T$ to $V$ is:

$A$ simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed at a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

Two light strings,each of length $\ell$,are fixed at points $A$ and $B$ on a fixed horizontal rod $xy$. $A$ small bob is tied by both strings and is in equilibrium,the strings are making an angle of $45^{\circ}$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released,then the period of the resulting small oscillation will be: