Coupled Oscillator: Coupled Mass-Spring System with Damping: Difference between revisions
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For mass 2: |
For mass 2: |
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<math> + \uparrow \sum F_{y_2} = m_2 \ddot{x}_2 \Rightarrow\ m_2 \ddot{x}_2=-2b_2\dot{x} |
<math> + \uparrow \sum F_{y_2} = m_2 \ddot{x}_2 \Rightarrow\ m_2 \ddot{x}_2=-2b_2\dot{x}_2-k_2s_2+m_2g</math> |
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Revision as of 15:07, 29 November 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.
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:
For the cases above
and
where l is the unstretched length of the spring and x is the displacement of the spring.
So if we put the equations above into the correct form we have:
and