Vibration of a mass-spring-damper system

Beijing Institute of Technology | Ming-Jian Li

The following MATLAB code is a companion code for the course on Artificial Intelligence and Simulation Science. It functions to calculate the vibration of a mass point under the action of spring force, external excitation, and damping, with time integration performed using the forward Euler method.

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clear; clc;
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m=0.1;
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k=2; 
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% forced vibration
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Fmag=0.1;  
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% natrual = sqrt(k/m)/2/pi 
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% 0.7118 will cause resonance
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freq=1;  
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omg=freq*2*pi;
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% damp
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c=0;
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% time
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dt = 0.1;  
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tend = 10;
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t_ = 0 : dt : tend;
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d = zeros(length(t_), 1);
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d(2) = 0.001;
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a=k*d(2);
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d(1) = d(2)+dt^2/2*a;
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for n = 2 : length(t_)-1
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    t = t_(n);
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    F = Fmag*cos(omg*t);
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    rhs = F - (k-2/dt^2*m)*d(n) - (m/dt^2-c/2/dt)*d(n-1);
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    coef = m/dt^2 + c/2/dt;
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    d(n+1) = rhs/coef;
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    clf
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    plot(t_, d, 'k', "LineWidth", 1.5)
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    hold on
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    pause(0.01);
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end

The result is as follows. With different input parameters, the vibration differs a lot.