Use the back button in your browser to exit from a program. This page is still under construction and the programs are living in two different places. Let me know if you have any issues.

Number	Description
Chapter 1: Harmonic Oscillation
1-1	The connection between harmonic motion and uniform circular motion.
1-2	Multiplication in the complex plane. Move the complex number z around in the complex plane with the arrow keys.
Chapter 2: Forced Oscillation and Resonance
2-1	A damped forced harmonic oscillator with one degree of freedom.
Chapter 3: Normal Modes
3-1	Two coupled pendulums.
Chapter 4: Symmetries
4-1	Beats in two coupled pendulums.
4-2	Modes of the hacksaw oscillator.
Chapter 5: Waves
5-1	Standing waves in a system of coupled pendulums with fixed ends.
5-2	Standing waves on a beaded string with fixed ends.
5-3	Standing waves on a beaded string with one free end.
Chapter 6: Continuum Limit and Fourier Series
6-1	Normal modes of the continuous string with fixed ends, with k = nπ/L for n = 1 to ∞. The up and down arrow keys increase n.
6-2	Normal modes of the continuous string with one fixed end and one free end, with k = nπ/L ‐ π/2L for n = 1 to ∞. The up and down arrow keys increase n.
6-3	The Fourier series for the function of (6.19)
6-4	Plucking an ideal string.
6-5	Same program as 6-4, but with variable inputs.
Chapter 7: Longitudinal Oscillations and Sound
7-1	Longitudinal modes of a continuous spring with fixed ends.
7-2	Longitudinal modes of a continuous spring with one fixed end and one free end.
Chapter 8: Traveling Waves
8-1	A traveling wave with a circle moving along the maximum of the wave at the phase velocity.
8-2	A traveling wave built out of two standing waves.
8-3	A traveling wave with damping. It peters out as it travels.
8-4	A forced oscillation problem for a continuous string with damping and one end fixed.
8-5	A forced oscillation problem for a beaded string with damping and one end fixed.
8-6	High- and low-frequency cut-offs in a forced oscillation problem.
Chapter 9: The Boundary at Infinity
9-1	Looking at reflected waves. You can see the uneven motion of a traveling wave with a small reflected amplitude.
9-2	Reflection and transmission from a mass on a string.
Chapter 10: Signals and Fourier Analysis
10-1	A triangular pulse propagating on a stretched string.
10-2	Group velocity (sum of two cosines).
10-3	Scattering of a pulse by a boundary between regions of different k.
10-4	Scattering of a pulse by a mass on a string.
Chapter 11: Two and Three Dimensions
11-1	The modes of a two-dimensional beaded string.
11-2	Snell’s law with no reflection.
11-3	Water sloshing in a rectangular container.
11-4	Two immiscible liquids sloshing. Note the mismatch between the upper and lower liquids in the middle. This is the result of the nonlinearity of the constraint of incompressibility.
Chapter 12: Polarization
12-1	Polarization in the two-dimensional harmonic oscillator, or in an electromagnetic wave. This shows the position of a string stretched in the z direction. The transverse position is shown in the x-y plane along with the x and y components. Alternatively, this can represent Ex and Ey in the electromagnetic wave propagating in the z direction and the total E field. In the upper left-hand corner is the complex two dimensional vector, that describes the polarization. You can change u1 between 1 and 0 with the left and right arrows. You can change |u2| between 1 and 0 with the up and down arrows. F1 and F2 decrease and increase the phase of u2 between π and -π.
12-2	The wandering of the electric field in unpolarized light. The electric field direction in the x-y plane is indicated by the trace. The color of the line changes occasionally to make it visible.
Extra Special Bonus Programs
Rainbow	Demonstration of red and blue light refracting in a raindrop.
Rainbow 2	Visualization of the double rainbow and Alexander’s dark band.
Water20	Water waves in an infinite ocean.
Lens	Light refracting through a lens.
X-ray	The relationship between color and phase in x-ray diffraction.
X-ray 2	A demonstration of x-rays diffracting through a crystal.
Purcell	The electric field generated by a particle that starts moving.
Purcell 2	The electric field generated by a particle that stops moving.
Chladni plates	The vibrational modes of a chladni plate.
Accelerometer spring	MOBILE ONLY– lock your phone in portrait mode for best results. Displays a mass on a spring that you can control using your phone’s accelerometer.

This work is licensed under CC BY-NC-ND 4.0