please help using matlab

The pendulum without small angle approximation (submit two Matlab files) The equation of motion for the pendulum may be written as = -122 sin , (3) do/dt = 0 where 0 is the angle with the normal, = d20/dt>, and Vg/L is the natural frequency of the pendulum. (a) Write a Matlab program that solves the differential equations for the pendulum and displays the angle 0 as a function of time, the angular velocity w as a function of time, and the phase space plot, w vs. 0. Please do not use the small angle approximation for this problem, we will look at large and small angles. Please use the following variable names: theta for the angle e omega for the angular velocity w = omeganat for the natural frequency N = Vg/L Since the natural frequency sets the time scale, a useful choice is N2 = 27 s-, which gives a period of 1 second. (b) Start by setting the initial conditions to 60 = -0.02 * 7 and wo = 0. Choose a final time ty of several periods. Before you run your program, determine what the graphs (0(t), wit), and phase-space plot) should look like. Run the program and compare the result with your expectation; resolve any discrepancies before you proceed further. (c) Now keep wo = 0, and start the pendulum at large angles, first use 0o = 0.5 *T, then 0. = 0.999 * 7. Please increase the final time so that you capture the full cycle of the motion. To what positions of the pendulum do these initial angles correspond? Please draw sketches (by hand is fine) of the pendulum to show the initial positions corresponding to the angles. Compare the large angle Matlab graphs with those from (b) paying special attention to the phase-space plots. A figure containing all three phase space plots may be helpful, but is not required. Please note, just as in the case of damped harmonic motion, the default accuracy of Matlab's ODE solver is not sufficient. To decrease the tolerance to 10-6 for both absolute and relative tolerance, you write options = odeset ('RelTol',1.e-6, AbsTol',1.e-6); The pendulum without small angle approximation (submit two Matlab files) The equation of motion for the pendulum may be written as = -122 sin , (3) do/dt = 0 where 0 is the angle with the normal, = d20/dt>, and Vg/L is the natural frequency of the pendulum. (a) Write a Matlab program that solves the differential equations for the pendulum and displays the angle 0 as a function of time, the angular velocity w as a function of time, and the phase space plot, w vs. 0. Please do not use the small angle approximation for this problem, we will look at large and small angles. Please use the following variable names: theta for the angle e omega for the angular velocity w = omeganat for the natural frequency N = Vg/L Since the natural frequency sets the time scale, a useful choice is N2 = 27 s-, which gives a period of 1 second. (b) Start by setting the initial conditions to 60 = -0.02 * 7 and wo = 0. Choose a final time ty of several periods. Before you run your program, determine what the graphs (0(t), wit), and phase-space plot) should look like. Run the program and compare the result with your expectation; resolve any discrepancies before you proceed further. (c) Now keep wo = 0, and start the pendulum at large angles, first use 0o = 0.5 *T, then 0. = 0.999 * 7. Please increase the final time so that you capture the full cycle of the motion. To what positions of the pendulum do these initial angles correspond? Please draw sketches (by hand is fine) of the pendulum to show the initial positions corresponding to the angles. Compare the large angle Matlab graphs with those from (b) paying special attention to the phase-space plots. A figure containing all three phase space plots may be helpful, but is not required. Please note, just as in the case of damped harmonic motion, the default accuracy of Matlab's ODE solver is not sufficient. To decrease the tolerance to 10-6 for both absolute and relative tolerance, you write options = odeset ('RelTol',1.e-6, AbsTol',1.e-6)