A simple pendulum consists of a brass sphere of mass = 1 kg suspended on a strin

Question

A simple pendulum consists of a brass sphere of mass = 1 kg suspended on a string of length l = 1 m. The pendulum oscillates with an amplituide of A = 1 cm and a period of T = 2 seconds.
Which of the following alterations will change the period to T = 1 second?
a Using a longer string of length l = 4 m
b Using a lighter brass sphere of mass m = 0.25 kg
c Reducing the amplitude to A = 0.25 cm
d Using a heavier brass sphere of mass m = 4 kg
e Using a shorter string of length l = 0.5 m
f Using a shorter string of length l = 0.25 m
g Using a longer string of length l = 2 m

Explanation / Answer

For a simple pendulum and assuming small angle approximation applies, the period of oscillation is independent of mass. The period of oscillation can be expressed as T = [2 pi][sqrt(L/g)], where T = period of oscillation. L = length of string. g = acceleration of gravity. Solving for L, L = g(T/2pi)^2 substituting T = 1 L = 9.8(1/2pi)^2 = 0.25 The answer is 1. Use a string of length L' = 0.25m

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