$A$ pendulum suspended from the ceiling of a train has a period $T$,when the train is at rest. When the train is accelerating with a uniform acceleration $a$,the period of oscillation will

$A$ piece of wood has length,breadth and height,'$a$','$b$' and '$c$' respectively. Its relative density is '$d$'. It is floating in water such that the side '$a$' is vertical. It is pushed down a little and released. The time period of $S.H.M.$ executed by it is ($g=$ acceleration due to gravity).

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

$A$ $50 \ cm$ long simple pendulum is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3} \ g \ m/s^2$. The time period of small oscillations of the pendulum about its equilibrium position is $.... \ s$ $\left(g=\pi^2 \ m/s^2\right):-$

The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$,is given by

What is the velocity of the bob of a simple pendulum at its mean position,if it is able to rise to a vertical height of $10\,cm$ $(g = 9.8\,m/s^2)$?