- How to approximate error in approximate derivatives
- How to approximate derivatives using forward difference methods
- How to approximate derivatives using backward difference methods
- How to approximate derivatives using central difference methods
- How to approximate higher order derivatives with forward, backward, and
- central differences
- The difference between a PDE and an ODE
- How to approximate differential equations with boundary conditions
- Solve steady-state heat transfer problem
- Solve static deflection of elastic beam
- Demonstrate convergence of finite difference solutions
- How to set up and solve an eigenvalue problem
- How eigenvalues and eigenvectors relate to natural frequencies and mode shapes
- How to turn a PDE into a finite difference ODE
- How to use eigenvalues to calculate natural frequencies of a vibrating string
- How to solve a coupled set of ODEs
- Visualize solutions to finite difference equations with 3D plots and
- animations
- How to listen to vibration solutions
In this final project, you will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:
| string | density (g/m) | tension (kg) |
|---|---|---|
| E | 0.401 | 7.28 |
| B | 0.708 | 7.22 |
| G | 1.140 | 7.32 |
| D | 2.333 | 8.41 |
| A | 4.466 | 9.03 |
| E | 6.790 | 7.71 |