Coupled Oscillator: Coupled Mass-Spring System with Damping

Problem Statement

For the below system set up a set of state variable equations, and then solve using Laplace transformations.

Fig. 1

Initial Values

For the upper mass:

$m_{1}=80kg{\frac {}{}}$

$k_{1}=60000{\frac {N}{m}}$

$b_{1}=0.1{\frac {}{}}$

And for the lower mass:

$m_{2}=400kg{\frac {}{}}$

$k_{2}=120000{\frac {N}{m}}$

$b_{2}=0.2{\frac {}{}}$