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Standard XIII

Physics

Forced Oscillations

Four pendulum...

Question

Four pendulums $A, B, C$ and $D$ are suspended from the same elastic support as shown in figure. $A$ and $C$ are of the same length, while $B$ is smaller than $A$ and $D$ is larger than $A$ . If $A$ is given a transverse displacement,

[Assume there is no loss of energy]

D

will vibrate with maximum amplitude

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C

will vibrate with maximum amplitude

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B

will vibrate with maximum amplitude

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All the four will oscillate with equal amplitude

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Solution

The correct option is B $C$ will vibrate with maximum amplitude
According to the question, $A$ is given tranverse displacement.

Through the elastic support, the disturbance is transferred to all the pendulums.
$A$ and $C$ have same length, hence they will be in resonance, because their time period of oscillation, $T = 2 π \sqrt{\frac{l}{g}}$ and hence angular frequency are the same.
So, amplitude of $A$ and $C$ will be maximum.

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Forced Oscillations

Standard XIII Physics

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Four pendulums A,B,C and D are suspended from the same elastic support as shown in figure. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement, [Assume there is no loss of energy]

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[Assume there is no loss of energy]