First slide

Periodic Motion

Question

Two simple pendulums of lengths 1 m and 16 m respectively are both given small displacements in the same direction at the same instant. They will again be in phase after the shorter pendulum has completed n oscillations where n is

Moderate

A

1/ 4
B

4 /3
C

4
D

5

Solution

$T_{1} = 2 π \sqrt{(\frac{1}{g})} and T_{2} = 2 π \sqrt{(\frac{16}{g})} ∴ \frac{T_{2}}{T_{1}} = 4 or \frac{v_{2}}{v_{2}} = 4 Now \frac{v_{1}}{v_{2}} - 1 = 4 - 1 or \frac{v_{1} - v_{2}}{v_{2}} = 3 The two pendulums will swings together again if v_{1} - v_{2} = 1 or \frac{1}{v_{2}} = 3 or v_{2} = \frac{1}{3} ∴ v_{1} = 1 + v_{2} = 1 = \frac{1}{3} + \frac{4}{3}$

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