First slide

Simple hormonic motion

Question

Two pendulums of lengths 1.44 and 1 metre length start swinging together. After how many vibrations of the longer pendulum will they again start swinging together ?

Moderate

A

3
B

4
C

5
D

6

Solution

$T_{i} = 2 π \sqrt{\frac{1.44}{g}} & T_{2} = 2 π \sqrt{\frac{1}{g}}$
Let shorter pendulum make n vibrations. Then longer will make one less than n to come in phase again
$i.e. {nt}_{2} = 2 (n - 1) t_{1} n \times 1 = (n - 1) \frac{12}{10}$
$n^{} = 6 n' = n - 1 = 6 - 1 = 5$

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