GRE GR 1777, Problem 003 Solution

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Physics GRE GR 1777
3. Classical Mechanics (Oscillations)
Solution) Angular frequency : \omega = \frac{2\pi}{T}
Period : T = \frac{2\pi}{\omega}
In the simple harmonic pendulum, \omega = \sqrt{\frac{g}{L}}
where L is the length of the pendulum.
Using above equations, T = 2\pi \sqrt{\frac{L}{g}}, then we can see that L \propto T^2.
Since T_{B} = 2 T_{A}, T_{A} : T_{B} = 1 : 2.
Then L_{A} : L_{B} = T^2_{A} : T^2_{B} = 1 : 4, therefore L_{B} = 4 L_{A}.
The answer is (E).

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