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 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.

Data from in problem 23.10

23.10 The oscillations of a swinging pendulum can be sim- ulated with the following nonlinear model: d0 d1 + sin 0 = 0 0 where = the angle of displacement, g = the gravitational constant, and I = the pendulum length. For small angular displacements, the sin is approximately equal to and the model can be linearized as d0 dt +0=0 Use ode45 to solve for as a function of time for both the linear and nonlinear models where 1 = 0.6 m and g = 9.81 m/s. First, solve for the case where the initial condition is for a small displacement (0 = 7/8 and de/dt = 0). Then repeat the calculation for a large displace- ment (0 = 7/2). For each case, plot the linear and nonlinear simulations on the same plot.