Coupled Oscillator: Coupled Mass-Spring System with Input

Setup State Space Equation

Problem Statement

Find an input function such that the lower mass, $m_{1}$, is stationary in the steady state. Find the equation of motion for the upper mass, $m_{2}$.

The use of one spring between the masses is just a simplification of a multi-spring system, so the possibility of being off-kilter is neglected and just the vertical forces are considered.

Initial Conditions and Values

$m_{1}=140kg{\frac {}{}}$

$k_{1}=108000{\frac {N}{m}}$

$m_{2}=80kg{\frac {}{}}$

$k_{2}=80000{\frac {N}{m}}$

Let the initial conditions be zero for the time being.

Force Equations