solution

Call the length of the pendulum $L$, its mass $m$, and the initial and final angles $\theta_i$ and $\theta_f$, respectively.

We want to calculate the change in the mechanical energy and that'll give us the work done by frictional forces.

The initial and final kinetic energy of the ball is zero. So the change in mechanical energy is just $\Delta U ~=~ U_f -U_i$.

$\Delta U ~=~ mg\Delta y ~=~ mg (y_f - y_i)$. Using trigonometry we can express the difference in heights $\Delta y$ in terms of angles, so we have

$$W_{nc} ~=~ mgL(\cos\theta_f - \cos\theta_i) ~=~ -2.03 J$$ (1.36)