Hello. I'm working on a problem involving 3 masses connected by springs. One of the masses has a driving force Focos(wt). These masses move along a line.
Using the Euler-Lagrange equations (I know some simple classical mechanics) I have derived the equations of motion, shown below:
k is the spring constant, m is the mass of each of the three objects. The displacements from equilibrium for each object are given by x, y and z. At the end I just convert from equilibrium displacement to actual position by adding on the equilibrium positions
I have spent days trying to figure out how to solve them analytically but I have had no luck. I have been going through a method in Goldstein's Classical Mechanics but cannot get things to work I have put the equations into matrix form, hoping that will help. I would love any help
I have a numerical solution of this, and I am confident it is accurate, so I have a comparison ready