**VPython Tools:**

Chapter 2:

Chapter 3:

- Simple Harmonic Motion: kinetic, potential, and total energy.
- Damped Harmonic Motion: kinetic, potential, and total energy.

Chapter 4:

**Mathematica tools:**

Chapter 4:

- The van der Pol equation.
- The plane pendulum equation.
- Contour plot of the phase space of the plane pendulum.
- Chaos for the driven pendulum.
- Bifurcation diagrams.

Chapter 5:

**Excel tools (used in 2004)**:

Chapter 2:

Chapter 3:

- Simple-Harmonic motion in 2D due to a single force.
- Simple-Harmonic motion in 2D due to a multiple forces.
- Damped Harmonic motion.

Analytical solutons are only possible for high simplified systems. The dynamics of realistic systems usually requires numerical methods to describe the solutions.

This page includes links to various files that can be used to simulate the response of systems exposed to both internal and external forces. In addition, tools used to visualize the solutions of various equastions of motion are included..