MATLAB Script:
%%
clear
clc
%% Parameters
global m c k omega
m = 1;
k = 1;
zeta = [0 0.5 1.5];
omega_n = sqrt(k/m);
omega_vals = [0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25].*omega_n;
%% Simulating all cases
for i=1:length(zeta)
c = zeta(i)*2*sqrt(m*k);
for j=1:length(omega_vals)
omega = omega_vals(j);
[t,X] = ode45('eom',[0 100],[0; 0]);
SS(i,j) = X(end,1);
end
end
%% Plot of Steady State Value vs Omega
plot(omega_vals,abs(SS(1,:)))
hold on
plot(omega_vals,abs(SS(2,:)))
hold on
plot(omega_vals,abs(SS(3,:)))
xlabel 'Omega (rad/s)'
ylabel 'Magnitude of Steady State Value'
legend 'zeta = 0' 'zeta = 0.5' 'zeta = 1.5'
grid on
Function 'eom' (save as new script)
function X_dot = eom (t,x0)
global m c k omega
x1 = x0(1);
x2 = x0(2);
y = sin(omega*t);
x1_d = x2;
x2_d = -(k/m)*x1 -(c/m)*x2 + y;
X_dot = [x1_d;x2_d];
end
Graph of Steady State value vs Omega
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