Coupled Oscillator: Coupled Mass-Spring System with Input: Difference between revisions

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(New page: =Setup State Space Equation= ==Problem Statement== Find an input function such that the lower mass, <math>m_1</math>, is stationary in the steady state. Find the equation of motion for t...)
 
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==Problem Statement==
==Problem Statement==
Find an input function such that the lower mass, <math>m_1</math>, is stationary in the steady state. Find the equation of motion for the upper mass, <math>m_2</math>.
Find an input function such that the lower mass, <math>m_1</math>, is stationary in the steady state. Find the equation of motion for the upper mass, <math>m_2</math>.

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==
==Initial Conditions and Values==

Revision as of 21:52, 17 November 2009

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.

Initial Conditions and Values

Force Equations

State Space Equation

Solve Using Laplace Transform Method

Solve Using Eigenvalue-Eigenvector Method