Question

In the diagram $A,B,C,D$ are four pendulums suspended from the same elastic string $PQ$. The length of $A$ and $C$ are equal to each other while the length of pendulum $B$ is smaller than that of $D$. Pendulum $A$ is set into a mode of vibrations.
$\left(i\right)$ Name the type of vibrations taking place in pendulums $B$ and $D$?
$\left(ii\right)$ What is the state of pendulum $C$?
$\left(iii\right)$ State the reason for the type of vibrations in pendulums $B$ and $C$.

Answer 1

$\left(i\right)$ $B$ and $D$ would be in the state of force vibration.

$\left(ii\right)$ Since the length of pendulum $C$ is same as that of $A$ therefore it is in the state of resonance.

$\left(iii\right)$ The pendulum $C$ has its length same as that of $A$ therefore its natural time period is also same that of $A$ and both remain in same phase; so resonance takes place. But $B$'s length is lesser than the length of $A$ hence $B$ would vibrate with smaller amplitude.