# HaydenProject — AERO3220 HW4

Aerospace Engineering undergraduate homework project by **Hayden Molloy**.

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## Assignment

**Course:** AERO3220  
**HW:** 4  
**Topic:** Coupled two-mass spring-damper system — numerical simulation and analysis

The system models two vertically stacked masses connected by springs and a damper, with an external forcing function applied to the bottom mass. Five parameter cases are simulated by varying damping coefficient and forcing frequency.

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## Files

| File | Description |
|---|---|
| `AERO3220_HW4.m` | MATLAB simulation script |
| `AERO3220_HW4.pdf` | Professor's original assignment |
| `AERO3220_HW4_block_diagram.md` | System block diagrams including transfer-function form and state-space form |
| `MEMORY.md` | AI agent context file — read before making changes |
| `.gitignore` | MATLAB and macOS artifact exclusions |

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## Block Diagrams

`AERO3220_HW4_block_diagram.md` contains several views of the system:

- **Transfer Function Block Diagram** — gain blocks and `1/s` integrators showing the coupled dynamics
- **System Equations Diagram** — signal flow of the coupled differential equations
- **State Space Form** — `ẋ = Ax + Bu` with explicit A and B matrices
- **Program Flow Diagram** — how the MATLAB script executes
- **Solver Subsystem** — internals of the `eom_two_mass` function

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## Physics

Two coupled second-order ODEs:

$$\ddot{z}_1 = -\frac{k_1}{m_1}z_1 + \frac{k_1}{m_1}z_2$$

$$\ddot{z}_2 = \frac{k_1}{m_2}z_1 - \frac{k_1+k_2}{m_2}z_2 - \frac{b}{m_2}\dot{z}_2 + \frac{1}{m_2}u(t)$$

Solved numerically with MATLAB `ode45` over `t = [0, 200]` seconds for 5 forcing/damping cases.

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## For AI Agents

> **Before making any changes, read [`MEMORY.md`](MEMORY.md) for full session context**, including physics details, file descriptions, known rendering constraints for the Mermaid diagrams, and conversation history.
>
> After completing significant changes, **update `MEMORY.md`** — specifically the *Conversation History Summary* and any relevant sections — so future agents have accurate context.