Differential Equation with a Discontinuous Forcing Function

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Consider the equation , where
is a square-wave step function and
is the oscillation of a spring-mass system in resonance with the square-wave forcing function. The graph of
is drawn in purple and that of
in blue. Using Laplace transforms, this solution is more compact than using a Fourier series expansion of the forcing function.
Contributed by: Stephen Wilkerson (March 2011)
(United States Military Academy West Point, Department of Mathematics)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This example comes from [1], Section 5.6, Differential Equations with Discontinuous Forcing Functions.
Reference
[1] J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, New York: John Wiley and Sons, 2010.
Permanent Citation