First slide

Simple hormonic motion

Question

Two pendulum start oscillating in the same direction at the same time from the same mean position. Their time periods are respectively 2 s and 1.5 s. The phase difference between them, when the smaller pendulum has completed one vibration, will be

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{2}$
C

$\frac{2 π}{3}$
D

$\frac{3 π}{2}$

Solution

Smaller pendulum will be that for which time period is less, here 1.5 s. So when this completes one vibration, the bigger pendulum will complete its $\frac{3}{4}$ oscillation (because its time period is 2 s) i.e., it will be at its negative extreme position. Hence the smaller pendulum will be ahead by a phase of $\frac{π}{2}$ than bigger pendulum at this time.

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