Problem 3: (20%) Consider the same system as described in Problem 2. (3a) Create a MATLAB program similar to CSD_fig2p10_code.m or create a Python program similar to the the one listed on page 11 of MEM255Lecture 2B notes, to draw the Bode plot of the system V(s) G(s)= 0.5 F(s) s+0.1 with frequency ranging from 0.01 rad/s to 1 rad/s. On the graph, specify the values of the magnitude |G (jw) G(jw) in degrees for the following three frequencies: (6%) in dB and the phase = = 0.01 rad/s, = c = 0.1 rad/s, = = 1 rad/s. (3b) Assume the input is a sinusoidal function f(t) = cos @ct = cos 0.lt. Find and plot (using MATLAB or Python) the resulting steady-state sinusoidal response in the form of v(t) = Acos(@ct +0) using the information obtained from the Bode plot in (3a). On the graph, specify the amplitude change and the phase shift of v(t) = Acos(@ct + 0) relative to the input f(t). (3%) (3c) Assume the input is a sinusoidal function f(t) = cos @t = cos 0.0lt. Find and plot (using MATLAB or Python) the resulting steady-state sinusoidal response in the form of v(t) = Acos(@t+0) using the information obtained from the Bode plot in (3a). On the graph, specify the amplitude change and the phase shift of v(t) = Acos(t + 0) relative to the input f(t). (3%) (3d) Assume the input is a sinusoidal function f(t) = cos @t = cost. Find and plot (using MATLAB or Python) the resulting steady-state sinusoidal response in the form of v(t) = Acos(@t + 0) using the information obtained from the Bode plot in (3a). On the graph, specify the amplitude change and the phase shift of v(t) = Acos(@t + 0) relative to the input f(t). (3%) (3e) Comment on the frequency domain physical meaning of the system based on your observation of the results in (3a), (3b), (3c), and (3d). (5%)