Hi Teja,
I understand that you need assistance in drawing graphs for single degree of freedom system vibration. You would like help to create graphs of Displacement ratio (T.R.) versus frequency ratio, Force transmissibility versus frequency ratio, Maximum acceleration versus frequency ratio, and Steady state displacement (xp(t)) versus time. You would like these graphs to be plotted for at least 5 periods of oscillation.
Here is a sample code that can help you create the desired graphs:
% Define system parameters
k = 10; % Spring constant (N/m)
m = 1; % Mass (kg)
% Define frequency ratio
w = (0:0.1:5)*sqrt(k/m);
% Calculate displacement ratio
tr = 1./sqrt((1-(w.^2)));
% Calculate force transmissibility
ft = 1./sqrt((1-(w.^2)).^2+4.*(0.05.*w).^2);
% Calculate maximum acceleration
amax = (w.^2)./sqrt((1-(w.^2)).^2+4.*(0.05.*w).^2);
% Calculate steady state displacement
% xp is the amplitude of displacement
xp = (0:0.01:5).*sqrt(k/m);
% Define time vector for steady state displacement plot
t = linspace(0, 10, 1000);
% Plotting
figure
% Displacement Ratio plot
subplot(2, 2, 1)
plot(w, tr)
title('Displacement Ratio vs Frequency Ratio')
xlabel('Frequency Ratio (w/w_n)')
ylabel('Displacement Ratio (x/x_n)')
% Force Transmissibility plot
subplot(2, 2, 2)
plot(w, ft)
title('Force Transmissibility vs Frequency Ratio')
xlabel('Frequency Ratio (w/w_n)')
ylabel('Force Transmissibility (F_{out}/F_{in})')
% Maximum acceleration plot
subplot(2, 2, 3)
plot(w, amax)
title('Maximum Acceleration vs Frequency Ratio')
xlabel('Frequency Ratio (w/w_n)')
ylabel('Maximum Acceleration (a_{max}/a_{in})')
% Steady State Displacement plot
subplot(2, 2, 4)
for i = 1:length(w)
plot(t, xp(i).*sin(w(i).*t))
hold on
end
hold off
title('Steady State Displacement vs Time')
xlabel('Time (s)')
ylabel('Displacement (m)')
I hope this helps!
Best regards,
Suraj.
