Four pendulums A, B, C and D are suspended from the same elastic support as shown in figure. A and Care of the same length, while B is smaller than A and D is larger than A.If A is given a transverse displacement, then(a) D will vibrate with maximum amplitude(b) C will vibrate with maximum amplitude(c) B will vibrate with maximum amplitude(d) all the four will oscillate with equal amplitude
Question
Four pendulums A, B, C and D are suspended from the same elastic support as shown in figure. A and Care of the same length, while B is smaller than A and D is larger than A.If A is given a transverse displacement, then(a) D will vibrate with maximum amplitude(b) C will vibrate with maximum amplitude(c) B will vibrate with maximum amplitude(d) all the four will oscillate with equal amplitude
Solution
The phenomenon described in the question is known as resonance. Resonance occurs when an object is made to vibrate at its natural frequency, resulting in an increase in amplitude.
In this case, pendulums A and C are of the same length. Therefore, they have the same natural frequency. When pendulum A is given a transverse displacement, it starts to oscillate at its natural frequency. Since pendulum C has the same natural frequency, it will start to vibrate with the maximum amplitude due to resonance.
Pendulums B and D, being of different lengths, have different natural frequencies. Therefore, they will not resonate with pendulum A and will not vibrate with the same amplitude.
So, the correct answer is (b) C will vibrate with maximum amplitude.
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