A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle \(\alpha\). A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in figure. The maximum angle \(\theta\) which the string makes with the vertical after hitting the pin is :

\(\cos^{-1} {\frac{L \cos {\alpha}- l}{L-l}}\)

Since the pendulum started with no kinetic energy, conservation of energy implies that the potential energy at Q max Q_max must be equal to the original potential energy, i.e., the vertical position will be same. Therefore :

\(L \cos {\theta} = l + (L-l) \cos {\theta}\)

\(\Rightarrow \cos {\theta} = \frac{L \cos {\theta}-l}{L-l}\)

\(\Rightarrow \theta = \cos^{-1}{\frac{L \cos {\theta}-l}{L-l}}\)