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.
![Untitled.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/242424/Untitled.png)
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.
![Untitled.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/242425/Untitled.png)