Question

A simple pendulum has a time period $T=2\sec$ when it swings freely.The pendulum is hung as shown in the figure, so that only one-fourth of its total length is free to swing to the left of the obstacle.It is displaced to position $A$ and released.If it takes $\frac{x}{2}\sec$ to swing to extreme displacement B and return to $A$. Find $x($ Assume that displacement angle is always small$)$

Answer 1

Here time period depends upon length.

In first part till obstacle is not there time $=\frac{T}{2}=1second$

After obstacle length becomes $\frac{1}{4}$

So time period become $\frac{T}{2}$

Time elapsed will be $t^{{}^{\prime }}=\frac{T}{4}=0.5second$

So total time $=t+t^{{}^{\prime }}=1.5sec=\frac{3}{2}sec$