Physics
Study the diagram and answer the following:
(a) Arrange the following pendulums according to their natural frequencies (use < > =).
(b) If Pendulum Z is initiated into oscillation, which pendulum among the others will exhibit the highest amplitude of vibration?
(c) Give reasons for your answer.
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Answer
(a) Y < W < Z = X
(b) X
(c) As Z and X share identical natural frequencies, Z will resonate and vibrate with greater amplitude.
Explanation:
(a) Effective length = length of the thread + distance of center of gravity from point of contact of sphere.
Let, effective length of pendulum X = lx
effective length of pendulum Y = lY
effective length of pendulum Z = lZ
effective length of pendulum W = lW
For pendulum X, which is completely filled with water, and pendulum Z, which is completely hollow, the center of gravity will be at the center of the sphere due to uniform mass distribution.
For pendulum W, where water fills more than half of the sphere, the center of gravity will be below the geometric center of the sphere. Conversely, for pendulum Y, where water fills less than half of the sphere, the center of gravity will be even lower than that of pendulum W (or, "further below the geometric center").
Here, lY > lW > lZ = lX
"Greater the effective length, smaller the frequency."
Y < W < Z = X
(b) If pendulum Z is set into oscillation, pendulum X will exhibit the highest amplitude of vibration due to resonance
(c) When the natural frequency of Z matches the natural frequency of X, X will vibrate with a higher amplitude due to resonance.
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