Time vs displacement plot of a Transfer function
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I am trying to plot time vs displacement plot of a transfer function. It is a simple case of spherical body in a liquid hence excitation of a spherical body is being resisted by the (elastic and viscous properties of the liquid) Hence F excitation= F inertia + F (elastic) + F viscous.
The final transfer function is of the form below where Delta Q is the relative displacement between the body and the liquid where as Vm is the excitation velocity.
I have used this transfer function to find eigen frequency for this system. Now i wants to check if the system undergoes resonance at that eigen frequency. How to do it using matlab
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1679591/image.jpeg)
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sai charan sampara
2024-4-26
Hello Hassan,
The following code might help you:
%% parameters
R = 5e-6;
zeta= 0.2308;
iota= 1.3;
rhom= 997;
rhonu = 1.3*rhom;
BoK = 8.54E-01 ;
B1u = 6.03E-07 ;
B1K = 1.42E-06 ;
B2u = 6.65E-13;
B2k = 1.31E-13;
%% coefficients in numerator
n0 = 0;
n1 = 4/3*pi*(R^3)*zeta*iota*rhom;
%% coefficients in denominator
d0 = BoK;
d1 = B1u + B1K;
d2 = B2u + B2k + (4/3*pi*(R^3)*rhonu);
%% transfer function
num = [n1 n0];
den = [d2 d1 d0];
G = tf(num, den)
This gives the expression for the transfer function "G". Once the transfer function is obtained you can use the following code to obtain the eigen frequencies:
eigen_values=eig(G);
eigen_freq=abs(imag(eigen_values))
Once the eigen frequencies are obtained you can define the input signal as a sinusoid of the eigen frequency and pass it through the system using the "lsim" function in MATLAB. This gives the output signal and the required Amplitude vs Time plot.
You can learn more about the function "lsim" from this documentation:
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