phase as a function of frequency for forced oscillations in matlab

To find the phase as a function of frequency for forced oscillations in MATLAB, you need to calculate the phasor of the system's response. A phasor represents the amplitude and phase angle of a sinusoidal function, and it's a useful tool for analyzing forced oscillations.

Assuming you have the transfer function of the system, you can calculate the phasor using the bode function in MATLAB. Here's an example code snippet that demonstrates how to calculate the phase angle as a function of frequency:

main.m
% Define the system's transfer function
num = [1];
den = [1 1 1];
sys = tf(num, den);

% Define the frequency range
w = logspace(-2, 2, 1000);

% Calculate the magnitude and phase of the system's response
[mag, phase] = bode(sys, w);

% Plot the phase angle as a function of frequency
semilogx(w, phase);
xlabel('Frequency (rad/s)');
ylabel('Phase (deg)');
title('Phase vs. Frequency for Forced Oscillations');
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In this code snippet, we first define the transfer function of the system using its numerator and denominator coefficients. We then define a log-spaced frequency range using the logspace function, which generates 1000 points between 0.01 and 100 rad/s in this example. We then use the bode function to calculate the magnitude and phase of the system's response at each frequency point in the range.

Finally, we plot the phase angle as a function of frequency using the semilogx function, which creates a plot with a logarithmic x-axis. The result is a plot that shows how the phase angle of the system's response changes with frequency, which is a useful tool for understanding the behavior of forced oscillations in the system.