Add Hayden HW4 files and program flow block diagrams

2026-04-04 17:45:30 -05:00
parent c4d1a468f1
commit 19e5383a43
3 changed files with 297 additions and 0 deletions
--- a/AERO3220_HW4.m
+++ b/AERO3220_HW4.m
@@ -0,0 +1,207 @@
+% Hayden Molloy
+% AERO3220 HW4
+% Due 18 Feb 2026
+
+clear; close all; clc;
+
+
+%% Initial Parameters
+
+    k1 = 100;      % N/m
+    k2 = 50;       % N/m
+    m1 = 500;      % kg
+    m2 = 250;      % kg
+
+% Time Parameters
+    t0 = 0;
+    tf = 200;
+    dt = 0.01;
+    tspan = t0:dt:tf;
+
+% Initial conditions [z1 z1dot z2 z2dot]
+    x0 = [0; 0; 0; 0];
+
+% Initialize Force Functions
+    F_1  = @(t) 100;                 % N
+    F_2  = @(t) 100*sin(0.25*t);     % N
+    F_3  = @(t) 100*sin(0.50*t);     % N
+
+
+%% Define Cases and ODEs
+
+% CASE 1:
+    b = 100;
+    F = F_1;
+[t1,x1] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
+
+% Case 2:
+    b = 100;
+    F = F_2;
+[t2,x2] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
+
+% CASE 3:
+    b = 0;
+    F = F_2;
+[t3,x3] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
+
+% Case 4:
+    b = 100;
+    F = F_3;
+[t4,x4] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
+
+% Case 5:
+    b = 0;
+    F = F_3;
+[t5,x5] = ode45(@(t,x) eom_two_mass(t,x,m1,m2,k1,k2,b,F), tspan, x0);
+
+
+%% Report Results
+
+% Create Legend
+lgnd = { ...
+    'Case 1: F=100, b=100', ...
+    'Case 2: F=100sin(0.25t), b=100', ...
+    'Case 3: F=100sin(0.25t), b=0', ...
+    'Case 4: F=100sin(0.50t), b=100', ...
+    'Case 5: F=100sin(0.50t), b=0'};
+
+
+% Plot 1: Top mass displacement vs. Time
+figure(1);
+
+plot(t1,x1(:,1),'LineWidth',1.3); 
+hold on;
+plot(t2,x2(:,1),'LineWidth',1.3);
+plot(t3,x3(:,1),'LineWidth',1.3);
+plot(t4,x4(:,1),'LineWidth',1.3);
+plot(t5,x5(:,1),'LineWidth',1.3);
+grid on;
+xlabel('Time (s)');
+ylabel('z_1 (m)');
+title('Top Mass Displacement z_1(t)');
+legend(lgnd,'Location','southoutside');
+
+
+% Plot 2: Bottom mass displacement vs. Time
+figure(2);
+
+plot(t1,x1(:,3),'LineWidth',1.3); 
+hold on;
+plot(t2,x2(:,3),'LineWidth',1.3);
+
+plot(t3,x3(:,3),'LineWidth',1.3);
+
+plot(t4,x4(:,3),'LineWidth',1.3);
+
+plot(t5,x5(:,3),'LineWidth',1.3);
+
+grid on;
+xlabel('Time (s)');
+ylabel('z_2 (m)');
+title('Bottom Mass Displacement z_2(t)');
+legend(lgnd,'Location','southoutside');
+
+
+% Plot 3: Top mass velocity vs. Time
+figure(3);
+
+plot(t1,x1(:,2),'LineWidth',1.3); 
+hold on;
+plot(t2,x2(:,2),'LineWidth',1.3);
+
+plot(t3,x3(:,2),'LineWidth',1.3);
+
+plot(t4,x4(:,2),'LineWidth',1.3);
+
+plot(t5,x5(:,2),'LineWidth',1.3);
+
+grid on;
+xlabel('Time (s)');
+ylabel('dz_1/dt (m/s)');
+title('Top Mass Velocity z_1''');
+legend(lgnd,'Location','southoutside');
+
+
+% PLOT 4: Bottom mass velocity vs. Time
+figure(4);
+
+plot(t1,x1(:,4),'LineWidth',1.3); 
+hold on;
+plot(t2,x2(:,4),'LineWidth',1.3);
+
+plot(t3,x3(:,4),'LineWidth',1.3);
+
+plot(t4,x4(:,4),'LineWidth',1.3);
+
+plot(t5,x5(:,4),'LineWidth',1.3);
+
+grid on;
+xlabel('Time (s)');
+ylabel('dz_2/dt (m/s)');
+title('Bottom Mass Velocity z_2''');
+legend(lgnd,'Location','southoutside');
+
+
+% PLOT 5: z1(t) and z2(t)
+% (solid = z1, dashed = z2)
+
+c1 = [0 114 178]/255;
+c2 = [213 94 0]/255;
+c3 = [230 159 0]/255;
+c4 = [117 112 179]/255;
+c5 = [0 158 115]/255;
+
+figure(5);
+
+plot(t1,x1(:,1),'-','LineWidth',1.2, 'Color', c1); 
+hold on;
+plot(t1,x1(:,3),'--','LineWidth',1.2, 'Color', c1);
+
+plot(t2,x2(:,1),'-','LineWidth',1.2, 'Color', c2);
+plot(t2,x2(:,3),'--','LineWidth',1.2, 'Color', c2);
+
+plot(t3,x3(:,1),'-','LineWidth',1.2, 'Color', c3);
+plot(t3,x3(:,3),'--','LineWidth',1.2, 'Color', c3);
+
+plot(t4,x4(:,1),'-','LineWidth',1.2, 'Color', c4);
+plot(t4,x4(:,3),'--','LineWidth',1.2, 'Color', c4);
+
+plot(t5,x5(:,1),'-','LineWidth',1.2, 'Color', c5);
+plot(t5,x5(:,3),'--','LineWidth',1.2, 'Color', c5);
+
+grid on;
+xlabel('Time (s)');
+ylabel('Displacement (m)');
+title('Top and Bottom Mass Displacements');
+
+legend({ ...
+    'Case 1 z_1', ...
+    'Case 1 z_2', ...
+    'Case 2 z_1', ...
+    'Case 2 z_2', ...
+    'Case 3 z_1', ...
+    'Case 3 z_2', ...
+    'Case 4 z_1', ...
+    'Case 4 z_2', ...
+    'Case 5 z_1', ...
+    'Case 5 z_2'}, ...
+    'Location','eastoutside');
+
+
+%% Local ODE function
+function dx = eom_two_mass(t, x, m1, m2, k1, k2, b, Ffun)
+    z1    = x(1);
+    z1dot = x(2);
+    z2    = x(3);
+    z2dot = x(4);
+
+    u = Ffun(t);
+
+    % m1*z1ddot + k1*z1 - k1*z2 = 0
+    z1ddot = (-k1/m1)*z1 + (k1/m1)*z2;
+
+    % m2*z2ddot + b*z2dot + (k1+k2)*z2 - k1*z1 = u
+    z2ddot = (k1/m2)*z1 - ((k1+k2)/m2)*z2 - (b/m2)*z2dot + (1/m2)*u;
+
+    dx = [z1dot; z1ddot; z2dot; z2ddot];
+end
--- a/AERO3220_HW4.pdf
+++ b/AERO3220_HW4.pdf
--- a/AERO3220_HW4_block_diagram.md
+++ b/AERO3220_HW4_block_diagram.md
@@ -0,0 +1,90 @@
+# AERO3220 HW4 Program Flow Block Diagram
+
+```mermaid
+flowchart TD
+    A([Start Script]) --> B[Clear Workspace: clear, close all, clc]
+    B --> C[Set Parameters: k1, k2, m1, m2]
+    C --> D[Set Time Grid: t0, tf, dt, tspan]
+    D --> E[Set Initial State: x0 = [z1 z1dot z2 z2dot]^T]
+    E --> F[Define Input Force Functions: F1, F2, F3]
+
+    F --> G[Case 1: b=100, F=F1]
+    G --> H[Run ode45 with eom_two_mass]
+
+    H --> I[Case 2: b=100, F=F2]
+    I --> J[Run ode45 with eom_two_mass]
+
+    J --> K[Case 3: b=0, F=F2]
+    K --> L[Run ode45 with eom_two_mass]
+
+    L --> M[Case 4: b=100, F=F3]
+    M --> N[Run ode45 with eom_two_mass]
+
+    N --> O[Case 5: b=0, F=F3]
+    O --> P[Run ode45 with eom_two_mass]
+
+    P --> Q[Build Legend Strings]
+    Q --> R[Plot Figure 1: z1 vs time (5 cases)]
+    R --> S[Plot Figure 2: z2 vs time (5 cases)]
+    S --> T[Plot Figure 3: z1dot vs time (5 cases)]
+    T --> U[Plot Figure 4: z2dot vs time (5 cases)]
+    U --> V[Plot Figure 5: z1 and z2 together by case]
+
+    V --> W[Local Function: eom_two_mass(t,x,...)]
+    W --> X[Unpack States: z1, z1dot, z2, z2dot]
+    X --> Y[Evaluate Input: u = Ffun(t)]
+    Y --> Z[Compute Accelerations: z1ddot and z2ddot]
+    Z --> AA[Return State Derivative: dx = [z1dot z1ddot z2dot z2ddot]^T]
+    AA --> AB([End])
+```
+
+## ODE Model Used in Each Case
+
+\[
+\ddot{z}_1 = -\frac{k_1}{m_1}z_1 + \frac{k_1}{m_1}z_2
+\]
+
+\[
+\ddot{z}_2 = \frac{k_1}{m_2}z_1 - \frac{k_1+k_2}{m_2}z_2 - \frac{b}{m_2}\dot{z}_2 + \frac{1}{m_2}u(t)
+\]
+
+where \(u(t)\) is one of the three forcing functions depending on the case.
+
+## Assignment-Style Block Diagram (Recommended For Submission)
+
+```mermaid
+flowchart TD
+    A([Start]) --> B[Define constants and masses: k1, k2, m1, m2]
+    B --> C[Define simulation time: t0, tf, dt, tspan]
+    C --> D[Set initial state vector: x0 = [z1 z1dot z2 z2dot]^T]
+    D --> E[Define force inputs: F1=100, F2=100sin(0.25t), F3=100sin(0.50t)]
+
+    E --> F[Create case table: (Case, b, Force)]
+    F --> G{i <= Number of Cases?}
+
+    G -- Yes --> H[Load case i values: b_i, F_i]
+    H --> I[Call ode45 with eom_two_mass and current case]
+    I --> J[Store outputs: t_i and x_i]
+    J --> K[i = i + 1]
+    K --> G
+
+    G -- No --> L[Generate legend labels]
+    L --> M[Plot z1 vs time for all cases]
+    M --> N[Plot z2 vs time for all cases]
+    N --> O[Plot z1dot vs time for all cases]
+    O --> P[Plot z2dot vs time for all cases]
+    P --> Q[Plot combined z1 and z2 by case]
+    Q --> R([End])
+```
+
+### Solver Subsystem (Inside `eom_two_mass`)
+
+```mermaid
+flowchart LR
+    A1[Inputs: t, x, m1, m2, k1, k2, b, Ffun] --> A2[Unpack states: z1, z1dot, z2, z2dot]
+    A2 --> A3[Compute input force: u = Ffun(t)]
+    A3 --> A4[Compute z1ddot from mass 1 equation]
+    A4 --> A5[Compute z2ddot from mass 2 equation]
+    A5 --> A6[Assemble derivative: dx = [z1dot z1ddot z2dot z2ddot]^T]
+    A6 --> A7[Return dx to ode45]
+```