Compute and plot the response of a simple pendulum with viscous damping whoseequation of motion is given by0.. .ml 2 ? + c? + mgl? =Compute the value of the damping coefficients for ? = 0.1.The initial conditions are? (0) = {15°, 30°, 45°, 60°, 90°} and (0) 0.? = . M = 10 g ; l = 5 cms.b) Compare the generated plot with Non-linear plot for each value of ?(0).What do you infer from the plots obtained?
c) Plot the natural frequency of the nonlinear solution versus initial condition ?(0).(Note: Plot the linear and the nonlinear curve in the same plot. Remember to convert the initialvalues of theta given in degrees, to radians.)Also make sure that the difference between the linear and the non-linear responses can be clearlyseen from the plot. If necessary use the zoom feature in order to show the difference.