Simulation of waves on a string. The string consists of points connected to their adjascent neighbors via the force function F(r). Additionally, each point may experience a restoring force, F(x), relative to the central line, and a damping force, F(v), relative to it's velocity. The points on the string can move transversely in 2D. A stimulus is applied by shaking the left end of the string according to the function f(t), which is defined in terms of it's radial and angular components. The f-> button specifies the meaning of f, whether it be an applied force on or the actual position of the left-most point on the string. a is a free variable for use in the equations. x-Scale zooms in vertically on the string, while t-Scale actually changes the time-step of the simulation (which may change behavior). The right-most button allows you to specify whether the endpoints of the string are open or fixed.

Enter key resets the simulation.
Ctrl key toggles pause.
ViEW PANELS:

• The string is the multi-colored line in the black window. Click and drag to get a different perspective.
• Below the string are plotted it's magnitude (gray) and helicity (red). Helicity indicates which way the string is wrapping around the central axis.
• The plot on the left shows the intensity spectrum of the waves on the string in the vertical (red) and out-of-screen (blue) directions.

NOTES:

• Nonzero dispersion exists only when both F(r) and F(x) are nonzero.
• Solitons can be produced by adding a nonlinear (cubic) component to F(x) that appropriately counteracts dispersion.
• Dropping t-scale suddenly causes a wave to emit a smaller copy in the backward direction. Apparently back-reflection can be produced by a numerical artifact.