Initial Commit

main.m

@@ -0,0 +1,55 @@
+%% Find log decrement
+
+m = 2000; %kg
+x1 = 0.09; %m
+x3 = 0.017; %m
+num_cycles = 2;
+log_decrement = (1/num_cycles)*log(x1/x3);
+
+zeta = log_decrement/(2*pi);
+
+tau_d = 0.14; %s
+omega_d = 2*pi/tau_d;
+
+omega_n = omega_d/sqrt(1-zeta^2);
+
+c = zeta*2*m*omega_n;
+disp("C value: ");
+disp(c);
+k = omega_n^2*m;
+disp("K value: ");
+disp(k);
+
+%% Part 2
+
+%k = 4028429; %N/m
+%c = 25000; %Ns/m 
+
+tspan = [0 1];
+initial_conditions = [0.09; 0];
+
+
+dydt_func = @(t,y) [y(2); -(c/m)*y(2)-(k/m)*y(1)];
+[t,y] = ode45(dydt_func, tspan, initial_conditions);
+plot(t, y(:,1));
+
+%% Amplitude and Phase Plot
+
+freq = linspace(0, 3*omega_n, 500);
+Y = 0.1; %m
+
+amplitude = Y*sqrt( (1 + (2*zeta*freq/omega_n).^2 )./ ( (1 - (freq/omega_n).^2 ).^2 + (2*zeta*freq/omega_n).^2 ) );
+figure();
+hold on;
+plot(freq, amplitude);
+plot([omega_n, omega_n], [0, 0.5]);
+hold off;
+
+phase_angle = atan2(2*zeta*(freq/omega_n).^3, 1-(freq/omega_n).^2+(2*zeta*freq/omega_n).^2);
+figure();
+hold on;
+plot(freq, phase_angle);
+plot([omega_n, omega_n], [0, pi]);
+hold off;
+
+