Question

Two simple pendulums, having periods of `2s` and `3s` respectively, pass through the mean position simulaneously at a particular instant. They may be in phase after an interval of:
A. `5s`
B. `6s`
C. `1s`
D. none of these above

Answer 1

Correct Answer - B
`omega_(1) = (2pi)/(2) = pi` and `omega_(2) = ((2pi)/(3))`
They will be in phase if
`(omega_(t) - omega_(2)) t = 0, 2pi, 4pi`…..
`t = (2pi)/((omega_(1) - omega_(2))) = (2pi)/(pi - (2pi)/(3)) = 6` sec