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

Force Equations

State Space Equation

Solve Using Laplace Transform Method