Question

Two simple pendulums have time periods $T$ and $5T/4$. They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when the pendulum with higher time period completes one oscillation is:

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

It is given that the first pendulum have time period $=T$ and
the second have time period have time period $\frac{5T}{4}=T+\frac{T}{4}$
This means that when second pendulum completes $1$ oscillation the first one completes $1+\frac{1}{4}$. First pendulum completes extra $\frac{1}{4}$ oscillation.
Therefore, phase difference is $\frac{2\pi }{4}={90}^0$