Coupled Oscillator: Coupled Mass-Spring System with Damping: Difference between revisions
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[[Image:HW-12.JPG|300px|thumb|right|Fig. 1]] |
[[Image:HW-12.JPG|300px|thumb|right|Fig. 1]] |
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=Solution= |
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==Initial Values== |
==Initial Values== |
Revision as of 11:34, 3 December 2009
Problem Statement
For the below system set up a set of state variable equations, and then solve using Laplace transformations. Assume all motion takes place in the vertical directions.
Solution
Initial Values
For the upper mass:
And for the lower mass:
Find the Force Equations
First we need to sum forces in the y-direction for each block.
For mass 1:
For mass 2:
So if we put the equations above into the correct form we have:
and
State Space Equation
The general form for the state equation is as shown below:
Where denotes a matrix and denotes a vector.
If we let , , , and be the state variables, then
We don't need to include gravity here if we allow are initial conditions for the spring to be zero with gravity accounted for.