Question

Study the diagram and answer the following:

1. Arrange the following pendulums according to their natural frequencies (use < > =).
2. If Pendulum Z is initiated into oscillation, which pendulum among the others will exhibit the highest amplitude of vibration?
3. Give reasons for your answer.

Answer 1

1. A pendulum’s natural frequency depends on its length, not on the mass or contents of its bob. The longer the pendulum, the lower its natural frequency. So arrange the pendulums from lowest to highest frequency in order from longest to shortest length, as shown in the diagram.
2. The pendulum with the same length as Z will have the highest amplitude of vibration.
3. Pendulums of equal length have equal natural frequencies. When Z oscillates, it produces a periodic force. The pendulum with the same natural frequency as Z resonates and therefore vibrates with the greatest amplitude. The contents or mass of the bobs do not change their natural frequencies.