Two simple pendulums A and B of time periods 2s and 2.1 s are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?

Question

Two simple pendulums A and B of time periods 2s and 2.1 s are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase? (A) 35 (B) 30 (C) 25 (D) 21

Tardigrade Admin · Accepted Answer

Pendulum having greater time period makes one oscillation less than the other. Since, both the pendulums will be in same phase after some time,
hence pendulum having greater time period

(T_{2} = 2.1 s)

makes one oscillation less than the other

(T_{2} = 2 s)

.
Time taken by pendulum

A

to make

n

oscillations is

2 n

Time taken by pendulum

B = 2.1 (n - 1)

Hence,

2 n = 2.1 (n - 1)

\Rightarrow n = \frac{2.1}{0.1} = 21

Q. Two simple pendulums A and B of time periods 2s and 2.1s are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?

35

30

25

21

Q. Two simple pendulums $A$ and $B$ of time periods $2 s$ and $2.1 s$ are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?