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:

$m_2=400kg\frac{}{}$

$k_2=120000\frac{N}{m}$

$b_2=0.2\frac{}{}$