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.

Problem Setup

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

FBD for m1

FBD for m2