Phase Difference Between Two Pendulums – Rankers Physics
Topic: Oscillation
Subtopic: Angular SHM and Simple Pendulum

Phase Difference Between Two Pendulums

Two pendulums have time periods T and \(\frac{5T}{4}\). They start SHM at the same time from the mean position. What will be the phase difference between them, when the smaller pendulum has completed one oscillation?
\(60^\circ\)
\(72^\circ\)
\(90^\circ\)
\(120^\circ\)

Solution:

For the smaller pendulum, time elapsed for one oscillation is \(t = T\), so its phase is \(2\pi\). The phase of the second pendulum is \(\phi_2 = \frac{2\pi}{5T/4}T = \frac{8\pi}{5}\). The phase difference is \(2\pi - \frac{8\pi}{5} = \frac{2\pi}{5} = 72^\circ\).

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