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, , is stationary in the steady state. Find the equation of motion for the upper mass, .

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


Let the initial conditions be zero for the time being.

Force Equations

State Space Equation

Solve Using Laplace Transform Method