Kevin S. Huang

2009: Problem 18

Topic: Oscillatory Motion
Concepts: Simple pendulum

Solution:

Recall the period of a simple pendulum is given by

T=2\pi\sqrt{\frac{l}{g}}

In our system, the pendulum oscillates as a simple pendulum of length $L$ half the time and as a simple pendulum of length $L/3$ half the time. Thus, the period is

T=\frac{T_1}{2}+\frac{T_2}{2}=\pi\sqrt{\frac{L}{g}}+\pi\sqrt{\frac{L}{3g}}=\pi\sqrt{\frac{L}{g}}\left(1+\frac{1}{\sqrt{3}}\right)

so the answer is E.

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Kevin S. Huang

2009: Problem 18

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2009: Problem 18

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