yes it is needed to be solved

Instructions (Assigned Problems): (1) For MATLAB problems, you must include both the input code and the output generated in the command window. Your presented solution should be clear, well-organized, and professional in appearance. Assignments that do not follow these guidelines will not be graded. (2) Create a single PDF file and upload it to Canvas. Assigned Problems AP1. Consider the pendulum system shown below, where L = 0.7 meters, m = 1.5 kg, g = 9.81 m/s? and e(t) is measured in radians. Pivot point Massless mod mass a. Show (by hand) that the motion of the pendulum is represented by the following dynamic equation: 8 (1) +2sin (8(t) = 0 b. Note that the differential equation above is nonlinear. When the equation is linearized about the equilibrium point (0) = 0, the linear time-invariant (LTI) model of motion is: 6(t) + (t) = 0 The linear approximation is valid for 0 (0) 1 rad. Use MATLAB to plot the LTI system responses for (0) = 15 deg and (0) = 30 deg from t = 0 to 10 seconds. Show both responses on the same graph. Include a legend and label the axes