Question

Find the period of oscillation of a pendulum of length $l$ if its point of suspension is moving horizontally with acceleration a.

Answer 1

We know that time period is given by

$T=2\pi \sqrt{\frac{l}{|g_{eff}|}}$ where $g_{eff}$ is the effective value of acceleration due to gravity.

Since $g$ (downwards) and $a$ (horizontal) are perpendicular to each other.

Here $|g_{eff}|=\sqrt{g^2+a^2}$

So $T=2\pi \sqrt{\frac{l}{\sqrt{g^2+a^2}}}$