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]

• 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

Answer 1

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, $T=2\pi \sqrt{\frac{l}{g}}$ and hence angular frequency are the same.
So, amplitude of $A$ and $C$ will be maximum.