A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration $a$, then the time period is given by $T = 2\pi \sqrt {\frac{l}{{g'}}} $, where $g'$ is equal to

lfa simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between $t = 0\ s$ to $t = \tau \ s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation ( due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta $ with the vertical

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise, then the loss in time of clock per day is ........... $s$

A simple pendulum is vibrating in an evacuated chamber, it will oscillate with

Two simple pendulums of equal length cross each other at mean position. What is their phase difference ?