Repeat Prob. 23.11, but for the nonlinear pendulum described in Prob. 23.10.

Data From Problem 23.11

Employ the events option described in Section 23.1.2 to determine the period of a 1-m long, linear pendulum (see description in Prob. 23.10). Compute the period for the fol following initial conditions: 

(a) θ = π / 8, 

(b) θ = π / 4, and 

(c) θ = π / 2. 

For all three cases, set the initial angular velocity at zero.