Question

two pendulums of lengths 100cm and 110.25cm start oscillating in phase. after how many oscillations will they again be in same phase?

Answer 1

Angular frequency of pendulum is given by

`\omega = \sqrt{(g)/(l)}`

for both pendulum we have

`\omega_1 = \sqrt{(9.81)/(1.00)}`

`\omega_1 = 3.13 rad/s`

For other pendulum

`\omega_2 = \sqrt{(9.81)/(1.1025)}`

`\omega_2 = 2.98 rad/s`

now we have relate angular frequency given as

[tex\omega_1 - \omega_2 = 3.13 - 2.98 = 0.15 rad/s[/tex]

now time taken to become in phase again is given as

`t = (2\pi)/(\omega_1 - \omega_2)`

`t = (2\pi)/(0.15) = 41.88 s`

now number of oscillations complete in above time

`N = (t)/((2\pi)/(\omega_1))`

`N = (41.88)/((2\pi)/(3.13))`

`N = 21 oscillation`