SHMHard
Question
Two pendulums at rest start swinging together. Their lengths are respectively 1.44 m and 1 m. They will again start swinging in same phase together after (of longer pendulum) :
Options
A.1 vibration
B.2 vibration
C.4 vibration
D.5 vibration
Solution
Let x1 = A1 sin ω1t and x2 = A2 sin ω2t
Two pendulums will vibrate in same phase again when there phase difference (ω2 − ω1)t = 2π
⇒ (
) t = 2π
⇒
= 2π (where n is number of vibrations completed by longer pendulum)
⇒
= 2π ⇒ n = 5
Thus after 5 vibrations of longer pendulum they will again start swinging in same phase.
Two pendulums will vibrate in same phase again when there phase difference (ω2 − ω1)t = 2π
⇒ (
) t = 2π⇒
= 2π (where n is number of vibrations completed by longer pendulum)⇒
= 2π ⇒ n = 5Thus after 5 vibrations of longer pendulum they will again start swinging in same phase.
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