Plotting amplitude and phase spectrum
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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?
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Thiago Henrique Gomes Lobato
2019-10-13
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.
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