Physics
In the figure shown below A, B, C and D are the four pendulums suspended from the same elastic string XY. The lengths of pendulum A and D are equal, while the length of pendulum B is shorter and of the pendulum C is longer. Pendulum A is set into vibrations.
(a) What is your observation about the vibrations of pendulum D?
(b) Give reason for your observation in part (a).
(c) What type of vibrations take place in pendulums B and C?
(d) Give reason for the answer in part (c)
Answer
(a) When pendulum A is set into vibrations, pendulum D also starts vibrating initially with a small amplitude and ultimately it acquires the amplitude same as pendulum A initially had.
When the amplitude of pendulum D becomes maximum, the amplitude of pendulum A becomes minimum because of the sharing energy by them.
Thereafter, the amplitude of pendulum B decreases and that of A increases. This process continues.
(b) Pendulum D is in state of resonance with pendulum A because the natural frequency of pendulum D is equal to that of A (as both have same length), and therefore there is an exchange of energy between the pendulums A and D.
When the amplitude of pendulum D increases, the amplitude of pendulum A decreases and vice versa. The pendulum D, therefore, vibrates with the frequency of pendulum A and it remains in phase with pendulum A.
(c) The vibrations of both pendulums B and C are of a very small amplitude.
(d) The length of pendulums B and C is not equal to the length of pendulum A, so they vibrate with small amplitude because they are under forced vibrations and not resonance.
Related Questions
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