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
What is meant by resonance? Describe a simple experiment to illustrate the phenomenon of resonance and explain it.
A vibrating tuning fork, held over an air column of a given length with its one end closed, produces a loud audible sound. Name the phenomenon responsible for it and explain the observation.
Figure below shows two tuning forks A and B of the same frequency mounted on two separate sound boxes with their open ends facing each other. The fork A is set into vibration. (a) Describe your observation. (b) State the principle illustrated by this experiment.
In figure given below, A, B, C and D represent the test tubes each of height 20 cm which are filled with water up to heights of 12 cm, 14 cm, 16 cm and 18 cm respectively. If a vibrating tuning fork is placed over the mouth of test tube D, a loud sound is heard.
(a) Describe the observations with the tubes A, B and C when the vibrating tuning fork is placed over the mouth of these tubes.
(b) Give the reason for your observation in each tube.
(c) State the principle illustrated by the above experiment.