Hello, I’m Hiroki🐶, a data scientist. In my previous blog, I introduced the Matlab code to solve the single degree of freedom vibration motion equation. I have modified it a bit more to represent it in terms of inputs and outputs, and I’d like to solve it this way.
First, this single degree of freedom vibration model. Normally, it can be written as a motion equation like this:
$$\begin{align*}
m\ddot{x}+c\dot{x}+kx&=f \
\end{align*}$$
Here,
$$\begin{align*}
f=c\dot{y}+ky& \
\end{align*}$$
The Matlab code to solve this model has been slightly modified from the previous code and is as follows:
% Definition of parameters
m = 1; % Mass [kg] ※Please set an appropriate value
k = 1; % Spring constant [N/m] ※Please set an appropriate value
c = 1; % Damping coefficient [N.s/m] ※Please set an appropriate value
% Definition of the differential equation
A = [0 1; -k/m -c/m];
B = [0; 1/m];
C = [1 0];
D = 0;
% Creation of the state space model
sys = ss(A, B, C, D);
% Simulation of the response
t = linspace(0, 50, 1000); % Simulation time [s]
% Applying external force f to the system
Y=1;
w0=sqrt(k/m);
f = c*Y*w0*cos(w0*t)+k*Y * sin(w0*t); % Time series of the external force
y = lsim(sys, f, t);
% Plotting the results
figure;
plot(t, y);
xlabel('Time [s]');
ylabel('Displacement [m]');
title('Response of the physical model');
grid on;
Upon execution, you might have obtained a graph like the one below.
This shows how easily and systematically you can determine the output x when inputting f into an M K C system.
In the following posts, I plan to apply this to more complex systems.
That’s it for today.
Thank you for reading until the end.
Love & Respect♡
Hiroki🐶