Please include matlab code. Thank you

This and some of the following problems concern models for the motion of a pendulum, which consists of a weight attached to a rigid arm of length L that is free to pivot in a complete circle. Neglecting friction and air resistance, the angle theta(t) that the arm makes with the vertical direction satisfies the differential equation theta" (t) + g/L sin (theta (t)) = 0, where g = 32.2 ft/sec^2 is the gravitational acceleration constant. We will assume the arm has length 32.2 ft and so replace (D.2) by the simpler form theta" + sin theta = 0. (Alternatively, one can rescale time, replacing t by Squareroot g/L t, to convert (D.2) to (D.3).) For motions with small displacements (theta small), sin almostequalto theta, and (D.3) can be approximated by the linear equation theta" + theta = 0. This equation has general solution theta (t) = A cos(t - delta), with amplitude A and phase shift delta. Hence all the solutions to the linear approximation (D.4) have period 2pi, independent of the amplitude A. In this problem we consider solutions of equation (D.3) satisfying the initial conditions theta(0) = A, theta'(0) = 0. If |A|