207 lines
4.2 KiB
Matlab
207 lines
4.2 KiB
Matlab
% Hayden Molloy
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% AERO3220 HW4
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% Due 18 Feb 2026
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clear; close all; clc;
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%% Initial Parameters
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k1 = 100; % N/m
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k2 = 50; % N/m
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m1 = 500; % kg
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m2 = 250; % kg
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% Time Parameters
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t0 = 0;
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tf = 200;
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dt = 0.01;
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tspan = t0:dt:tf;
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% Initial conditions [z1 z1dot z2 z2dot]
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x0 = [0; 0; 0; 0];
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% Initialize Force Functions
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F_1 = @(t) 100; % N
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F_2 = @(t) 100*sin(0.25*t); % N
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F_3 = @(t) 100*sin(0.50*t); % N
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%% Define Cases and ODEs
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% CASE 1:
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b = 100;
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F = F_1;
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[t1,x1] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
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% Case 2:
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b = 100;
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F = F_2;
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[t2,x2] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
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% CASE 3:
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b = 0;
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F = F_2;
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[t3,x3] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
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% Case 4:
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b = 100;
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F = F_3;
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[t4,x4] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
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% Case 5:
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b = 0;
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F = F_3;
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[t5,x5] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
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%% Report Results
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% Create Legend
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lgnd = { ...
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'Case 1: F=100, b=100', ...
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'Case 2: F=100sin(0.25t), b=100', ...
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'Case 3: F=100sin(0.25t), b=0', ...
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'Case 4: F=100sin(0.50t), b=100', ...
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'Case 5: F=100sin(0.50t), b=0'};
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% Plot 1: Top mass displacement vs. Time
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figure(1);
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plot(t1,x1(:,1),'LineWidth',1.3);
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hold on;
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plot(t2,x2(:,1),'LineWidth',1.3);
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plot(t3,x3(:,1),'LineWidth',1.3);
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plot(t4,x4(:,1),'LineWidth',1.3);
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plot(t5,x5(:,1),'LineWidth',1.3);
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grid on;
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xlabel('Time (s)');
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ylabel('z_1 (m)');
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title('Top Mass Displacement z_1(t)');
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legend(lgnd,'Location','southoutside');
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% Plot 2: Bottom mass displacement vs. Time
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figure(2);
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plot(t1,x1(:,3),'LineWidth',1.3);
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hold on;
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plot(t2,x2(:,3),'LineWidth',1.3);
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plot(t3,x3(:,3),'LineWidth',1.3);
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plot(t4,x4(:,3),'LineWidth',1.3);
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plot(t5,x5(:,3),'LineWidth',1.3);
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grid on;
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xlabel('Time (s)');
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ylabel('z_2 (m)');
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title('Bottom Mass Displacement z_2(t)');
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legend(lgnd,'Location','southoutside');
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% Plot 3: Top mass velocity vs. Time
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figure(3);
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plot(t1,x1(:,2),'LineWidth',1.3);
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hold on;
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plot(t2,x2(:,2),'LineWidth',1.3);
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plot(t3,x3(:,2),'LineWidth',1.3);
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plot(t4,x4(:,2),'LineWidth',1.3);
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plot(t5,x5(:,2),'LineWidth',1.3);
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grid on;
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xlabel('Time (s)');
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ylabel('dz_1/dt (m/s)');
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title('Top Mass Velocity z_1''');
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legend(lgnd,'Location','southoutside');
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% PLOT 4: Bottom mass velocity vs. Time
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figure(4);
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plot(t1,x1(:,4),'LineWidth',1.3);
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hold on;
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plot(t2,x2(:,4),'LineWidth',1.3);
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plot(t3,x3(:,4),'LineWidth',1.3);
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plot(t4,x4(:,4),'LineWidth',1.3);
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plot(t5,x5(:,4),'LineWidth',1.3);
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grid on;
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xlabel('Time (s)');
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ylabel('dz_2/dt (m/s)');
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title('Bottom Mass Velocity z_2''');
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legend(lgnd,'Location','southoutside');
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% PLOT 5: z1(t) and z2(t)
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% (solid = z1, dashed = z2)
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c1 = [0 114 178]/255;
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c2 = [213 94 0]/255;
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c3 = [230 159 0]/255;
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c4 = [117 112 179]/255;
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c5 = [0 158 115]/255;
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figure(5);
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plot(t1,x1(:,1),'-','LineWidth',1.2, 'Color', c1);
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hold on;
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plot(t1,x1(:,3),'--','LineWidth',1.2, 'Color', c1);
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plot(t2,x2(:,1),'-','LineWidth',1.2, 'Color', c2);
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plot(t2,x2(:,3),'--','LineWidth',1.2, 'Color', c2);
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plot(t3,x3(:,1),'-','LineWidth',1.2, 'Color', c3);
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plot(t3,x3(:,3),'--','LineWidth',1.2, 'Color', c3);
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plot(t4,x4(:,1),'-','LineWidth',1.2, 'Color', c4);
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plot(t4,x4(:,3),'--','LineWidth',1.2, 'Color', c4);
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plot(t5,x5(:,1),'-','LineWidth',1.2, 'Color', c5);
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plot(t5,x5(:,3),'--','LineWidth',1.2, 'Color', c5);
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grid on;
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xlabel('Time (s)');
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ylabel('Displacement (m)');
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title('Top and Bottom Mass Displacements');
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legend({ ...
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'Case 1 z_1', ...
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'Case 1 z_2', ...
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'Case 2 z_1', ...
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'Case 2 z_2', ...
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'Case 3 z_1', ...
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'Case 3 z_2', ...
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'Case 4 z_1', ...
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'Case 4 z_2', ...
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'Case 5 z_1', ...
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'Case 5 z_2'}, ...
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'Location','eastoutside');
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%% Local ODE function
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function dx = eom_two_mass(t, x, m1, m2, k1, k2, b, Ffun)
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z1 = x(1);
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z1dot = x(2);
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z2 = x(3);
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z2dot = x(4);
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u = Ffun(t);
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% m1*z1ddot + k1*z1 - k1*z2 = 0
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z1ddot = (-k1/m1)*z1 + (k1/m1)*z2;
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% m2*z2ddot + b*z2dot + (k1+k2)*z2 - k1*z1 = u
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z2ddot = (k1/m2)*z1 - ((k1+k2)/m2)*z2 - (b/m2)*z2dot + (1/m2)*u;
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dx = [z1dot; z1ddot; z2dot; z2ddot];
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end |