First slide

Simple hormonic motion

Question

Two pendulums of lengths 1.69 m and 1.44 m start swinging together. After how many vibrations will they again start swinging together?

Easy

A

8 vibrations
B

10 vibrations
C

12 vibrations
D

14 vibrations

Solution

$T_{1} = 2 π \sqrt{\frac{1.69}{g}}, T_{2} = 2 π \sqrt{\frac{1.44}{g}}$
Let shorter pendulum makes (n + I) vibrations then the longer makes n vibrations to come in phase again then
$(n + 1) T_{2} = {nT}_{1} \frac{n + 1}{n} = \frac{T_{1}}{T_{2}} = \sqrt{\frac{1.69}{1.44}} \Rightarrow n = 12$

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