Coupled Oscillator: Coupled Mass-Spring System with Input

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Setup State Space Equation

Problem Statement

Find an input function such that the lower mass, m1, is stationary in the steady state. Find the equation of motion for the upper mass, m2.

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
Problem Setup


Initial Conditions and Values

m1=140kg

k1=108000Nm

m2=80kg

k2=80000Nm


Let the initial conditions be zero for the time being.


Force Equations

FBD for m1
FBD for m1
FBD for m2
FBD for m2

State Space Equation

Solve Using Laplace Transform Method