Add Hayden HW4 files and program flow block diagrams

AERO3220_HW4_block_diagram.md

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+# 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]
+```