Plotting amplitude and phase spectrum

We have been given the Response of a mechanical sensor (seismometer) where:

We were then given the original frequency, f, damping, h, and gain factor, G. With this we are meant to be able to plot the amplitude and phase spectrum against frequency. I have no idea where to start, and have been looking at coding for Fourier transformations and polynomials for ages. Could anyone suggest where to start?

Answer 1

[Thiago Henrique Gomes Lobato]

This amplitude and phase spectrum plot of a transfer function is called the Bode plot , it is very well known and you may easily find some references online, this guy, for example, has some very nice tutorials about control engineering that may apply to your problem :https://www.youtube.com/watch?v=_eh1conN6YM&t=12s. In Matlab you have a tool to define the coefficients of your transfer function and then plot the result (as example of your equation):

% Parameters
G = 1;
h = 0.3;
w0 = 5;

% Generate the transfer function
numerator = [G,0,0];
denominator = [-1,-2*h*w0,w0^2];
sys = tf(numerator,denominator)

% Plot it
bode(sys)
grid

sys =
 
       -s^2
  --------------
  s^2 + 3 s - 25
 
Continuous-time transfer function.

I feel however about uneasy about your equation since it is not stable and I believe it should be a stable damped system. Maybe you had some typo erros? A more reasonable transfer function for a damped system would look like this

% Parameters
G = 1;
h = 0.3;
w0 = 5;

% Generate the transfer function
numerator = [w0^2*G];
denominator = [1,2*h*w0,w0^2];
sys = tf(numerator,denominator)

% Plot it
bode(sys)
grid

sys =
 
        25
  --------------
  s^2 + 3 s + 25
 
Continuous-time transfer function.