Coupled spring-mass-damper system with non-linear spring

Here is one last simulation for the mass-spring-damper system, with a non-linear spring. The following values were used for the simulation:

 

The initial values used were:

 

The patterns for this set of ODE’s are plotted below. Damping and the non-linear spring force appear to “compete” against each other! While the damper element tends to “dampen” out the vibrations with time (i.e., have the effect of reducing the amplitude of motion of the two masses with time), the non-linear spring effects take over in the sense of randomizing the movement of the masses.