Problem 2: The equation of motion of a pendulum whose base is accelerating horizontally with an acceleration a (which is a function of time), is given by: where 0 is the pendulum deflection angle with respect to the vertical Assume that the base acceleration (a) is linear with time, as given by the following relation: a kt Use MATLAB to numerically solve the above equation, and obtain plots of 0 versus time (0) for simulation time of 10 seconds, for the following two cases (on a single graph): Case l: k 0.3, Case 2: k 0.8. Use the following values and initial conditions (for both cases) 8 9.81 mls L 1.5 m, 0(0) 2 rad, 0_dot(0)0 rads