Taut String Driven At One End With Realistic Drag

Models numerically the motion of a taut string driven at one end with linear and nonlinear drag.

This script numerical integrates the hyperbolic wave equation describing transverse waves on a string with linear, quadratic, or realistic nonlinear drag. One end of the string is fixed and the other is forced with a periodic function. When the drive frequency matches a natural resonant frequency, a steady oscillation is established after a few damping times and standing waves appear at resopnant frequencies. The simulated string steady state motion is compared to the exact analytic solution in the case of harmonic forcing and linear drag, establishing the accuracy of the numerical method. Physical parameters are chosen to match a standard "standing waves on a string" educational lab. Drag simply proportional to the suqare of velocity, and drag with a Reynolds number dependent drag coefficient can be simulated.

The script illustrates a standard numerical method for solving a partial differential equation, and methods of generating an animation. It was based on osc-string_driven.m,by Ian Cooper, School of Physics, University of Sydney, Doing Physics with MATLAB. I have expanded his script to include physical parameters relevant to air drag, various forms of damping, and additional visualizations. The script may run faster if executed from the command line.

This script may interest students and instructors of physics and engineering. Try this suggestions are included for further exploration.