$A$ uniform rod of length $1.8 \,m$ suspended by an end is made to undergo small oscillations. Find the length of the simple pendulum having the mass and time period equal to that of the rod. (in $\,m$)

$A$ pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels the same distance per unit time,the period of oscillation is

$A$ person of mass $M$ is sitting on a swing of length $L$ and swinging with an angular amplitude $\theta_0$. If the person stands up when the swing passes through its lowest point,the work done by him,assuming that his centre of mass moves by a distance $l$ $(l << L)$,is close to

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

$A$ simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in the figure. As the pendulum moves from $A$ to the right,the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction,the point $D$

$A$ 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):