Q. Two simple pendulums of time period 2 sec and 2.1 sec are made to vibrate simultaneously. They are in phase initially. After how many vibrations they are in the same phase?

- 21
- 25
- 30
- 35

**Solutions:**

First simple pendulum has a time period of 2 sec.

Second pendulum has a time period of 2.1 sec.

That means: After each complete oscilation, the second pendulum is ahead by (2.1 – 2.0) = 0.1 sec.

if we show this in a list:

after 1 vibration, second pendulum leads by 0.1 s

after 2 vibrations, second pendulum leads by 2×0.1s = 0.2 s

after 3 vibrations, second pendulum leads by 3×0.1s = 0.3 s

………………………….

after 10 vibrations, second pendulum leads by 10×0.1s = 1s

after 20 vibrations, second pendulum leads by 20×0.1s = 2s

after 21 vibrations, second pendulum leads by 21×0.1s = 2.1s (This is a time period of second pendulum.)

So, both pendulum comes at mean position after 21 oscillations which means they are at the same phase.

**Ans:** 21

**OR,**

Difference of time period of two pendulum is (2.1 – 2.0)s = 0.1 s

Let’s say, both pendulum after completing complete oscillations, they come to same phase.

So,

**Ans:** 21