Question

Two simple pendulums of lengths 1.44 m and 1.96 m start swinging together. After how many vibrations will they again start swinging together?

Options

• 5 oscillations of smaller pendulum

• 6 oscillations of smaller pendulum

• 4 oscillations of bigger pendulum

• 6 oscillations of bigger pendulum

Answer 1

6 oscillations of bigger pendulum

Explanation:

We know that, frequency ofoscillations is,

n = `1/(2pi)  sqrt("g"/"l")`

`therefore "n"  alpha 1/sqrt("l")`

For given pendulums,

`"n"_1 = 1/(2pi)  sqrt("g"/1.44)`

and `"n"_2 = 1/(2pi)  sqrt("g"/1.96)`

`therefore  "n"_1/"n"_2 =  sqrt(1.96/1.44) = 7/6`

`therefore "n"_2 = (6"n"_1/7`

Hence, for n₂ to be an integer, the minimum value of n1 should be 7.

`"n"_2 = 6`

i.e., after 6 oscillations of a bigger pendulum, both will be in phase.