In structural dynamics many systems can be represented as variations on a simple pendulum. You may have learned the linearized equation for the dynamic behavior of a pendulum in physics; the true equation is d^2 theta/dt^2 + g/L sin theta = 0 where theta is the angle of the pendulum, L is the length of the rod or cable, t is time and g is the gravitational constant. As in class, we can rewrite the differential equation in a form that we can use in Matlab: theta_t+1 = 2 theta_t - theta_t-1 - delta t^2 * g/L sin (theta_t) The initial displacements theta_1 and theta_2 depend on the engineering situation under analysis, but they are known. Gravity is obviously known. The time step can be chosen reasonably freely. The one parameter the engineer has change the behavior of the pendulum is the length of the rod or cable. L is therefore a control parameter, and finding best rod length for a particular engineered system is a control problem. Write a Matlab script that implements equation (1) to estimate the position of the pendulum for t=0.1:10 seconds, using a delta t = 0.1 sec. Use an effective rod length of L = 10 m, and of course g = 9.81 m/s^2