Two Masses with Forcing Functions Oscillating between Three Springs

This Demonstration treats a system consisting of three springs connecting two masses between two walls with forcing functions on the masses, given by and . The solution plots are shown and dynamically updated to reflect changes to the initial displacements and the forcing frequencies. The short-term behavior can be affected by the changes in initial displacement, but the long-term behavior is dominated by the forcing functions. The two equations being solved are:

This example comes from [1], Section 6.6, Nonhomogeneous Linear Systems.

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.