Consider the 10-DOF spring/mass system shown below. An impulsive force is applied to the left-most particle in the system.

The response of the system can readily be found from a modal expansion, writing the response in terms of the discrete modal vectors of the system. A solution for a similar example to this can be found in the Chapter 5 material on the blog. In this solution, the higher modes make a significant contribution to the overall response.

Shown below is short clip showing system response using simulation data from the analytical solution described above. In particular, we are seeing the stretch/compression for the left-most spring (shown in * BLUE*) and for the right-most spring (shown in

*). Here we see that the deformation in the spring to the left responds immediately to the impact load. There is a time delay before the spring on the far right responds indicating that it takes a finite time for the wave to travel along the system. Note that the shape of the response is not preserved (the motion is NOT periodic). Had the natural frequencies of the system been integer-multiple harmonics of the fundamental, the shape of the traveling wave would have been preserved in time.*

**RED**