Ncert Exercises & Solutions

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

1.	$D$ will vibrate with maximum amplitude.
2.	$C$ will vibrate with maximum amplitude.
3.	$B$ will vibrate with maximum amplitude.
4.	All four will oscillate with equal amplitude.

2. Hint: The amplitude of the pendulums depends on their frequencies.

Step 1: Find the comparative frequency of the pendulum.

According to the question, A is given a transverse displacement.

Through the elastic support, the disturbance is transferred to all the pendulums.

A and C are having the same length, hence they will be in resonance because of their time period of oscillation.

T = 2 π \sqrt{\frac{l}{g}}

$T = 2 π \sqrt{\frac{l}{g}}$ and hence, the frequency is the same.

So, the amplitude of A and C will be maximum.

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