Plotting an FRF from a Transfer Function in MATLAB

Seeing the frequency response function (FRF) of a single-degree-of-freedom (SDOF) system is the fastest way to build structural-dynamics intuition. Here's a practical setup in MATLAB.

SDOF Parameters#

m = 1;          % mass [kg]
k = 1e4;        % stiffness [N/m]
zeta = 0.05;    % damping ratio [-]
 
wn = sqrt(k/m);             % natural angular frequency [rad/s]
c  = 2*zeta*sqrt(k*m);      % damping coefficient

FRF Computation and Plot#

f = linspace(0, 50, 2000);   % frequency [Hz]
w = 2*pi*f;
 
H = 1 ./ (k - m*w.^2 + 1i*c*w);   % receptance FRF
 
figure;
subplot(2,1,1);
semilogy(f, abs(H)); grid on;
ylabel('|H(\omega)|'); title('SDOF FRF');
 
subplot(2,1,2);
plot(f, angle(H)*180/pi); grid on;
xlabel('Frequency [Hz]'); ylabel('Phase [\circ]');

What to look for

You should see a clear peak at the natural frequency in the magnitude curve, and a 180° shift at the same point in the phase curve. As you increase damping, the peak gets lower and broader.

Running this small script while changing the parameters is one of the most effective ways to explain the relationship between resonance and damping.