Final answer:
The student is asked to use MATLAB to find the sinusoidal steady-state output for a given input on a linear circuit using the step response. A conceptual MATLAB code and explanation are provided to demonstrate how the response should be calculated and plotted.
Step-by-step explanation:
To find the sinusoidal steady-state output for the input x(t) = 20 cos(100t), we utilize the frequency response of the given linear circuit. Since the step response g(t) is given in terms of a sine function and a step function u(t), it indicates a second-order system with a resonance near 200 rad/s. However, the frequency of interest for the steady-state response is 100 rad/s. The MATLAB code to find the output y(t) would look like the following:
% Your Name
x_freq = 100; % Frequency of input in rad/s
x_amplitude = 20; % Amplitude of input signal
% Coefficients for system response at 200 rad/s
a = 2; % Amplitude scaling factor
b = 50; % Exponential decay
% Setup time vector
t = 0:0.001:0.1; % 0 to 0.1 seconds with 1 ms interval
% Calculate output
y = a * exp(-b * t) .* sin(x_freq * t);
% Plotting
figure;
plot(t, y);
title('Sinusoidal steady-state output');
xlabel('Time [s]');
ylabel('Amplitude [V]');
Note: The provided code snippet is a conceptual representation and may require adjustments based on the actual dynamics of the system which are not fully detailed in the question. After running the code, the plot produced will give a visual representation of the sinusoidal steady-state output y(t).