create a spring mass damper system in matlab

To create a spring mass damper system in MATLAB, we first need to define the differential equation governing the system's dynamics. The equation of motion for a spring-mass-damper system is given by:

main.m
m*x'' + c*x' + k*x = f(t)
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where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position over time t and f(t) is an external force applied to the system.

Now we can define this equation in a MATLAB function file. Let's name this file springMassDamper.m:

main.m
function xdot = springMassDamper(t, x, m, c, k, f)
    xdot = zeros(2,1);
    xdot(1) = x(2);
    xdot(2) = (1/m) * (f - c*x(2) - k*x(1));
end
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Here, we define the function springMassDamper with the input arguments t (time), x (state), m (mass), c (damping coefficient), k (spring constant), f (external force input). The output of the function xdot is the first and second derivative of the mass position x over time.

Now we can use MATLAB to simulate the system's response to various inputs. Let's say we want to simulate a system with the following parameters:

main.m
m = 1;      % mass in kg
c = 0.5;    % damping coefficient in Ns/m
k = 2;      % spring constant in N/m
f = 2;      % amplitude of external force in N
tspan = [0 20];     % simulation time in seconds
x0 = [0; 0];        % initial position and velocity
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To simulate the response of the system using ode45 (a MATLAB function for solving ordinary differential equations), we can call it like so:

main.m
[t,x] = ode45(@(t,x) springMassDamper(t, x, m, c, k, f), tspan, x0);
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This will return a matrix of time values t and mass position and velocity x.

We can plot the response of the system over time with the following code:

main.m
plot(t, x(:,1));
xlabel('Time (s)');
ylabel('Position (m)');
title('Spring-Mass-Damper System Response');
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This will produce a plot showing the displacement of the mass over time.