Laplace transforms: Critically Damped Motion: Difference between revisions
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Mark.bernet (talk | contribs) |
Mark.bernet (talk | contribs) |
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<math>\text {k=4}\,</math> |
<math>\text {k=4}\,</math> |
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<math>\text {C=4}\,</math> |
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<math>\text {x(0)=0}\,</math> |
<math>\text {x(0)=0}\,</math> |
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<math>\text {Standard equation: }\,</math> |
<math>\text {Standard equation: }\,</math> |
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<math>m\frac{d^2x}{dt^2}+C\frac{dx}{dt}+khx=0</math> |
<math>m\frac{d^2x}{dt^2}+C\frac{dx}{dt}+khx=0</math> |
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===Solving the problem=== |
===Solving the problem=== |
Revision as of 16:53, 18 November 2009
Using the Laplace Transform to solve a spring mass system that is critically damped
Problem Statement
An 8 pound weight is attached to a spring with a spring constant k of 4 lb/ft. The spring is stretched 2 ft and rests at its equilibrium position. It is then released from rest with an initial upward velocity of 3 ft/s. The system contains a damping force of 2 times the initial velocity.
Solution
Things we know
Solving the problem
Apply the Initial and Final Value Theorems to find the initial and final values
- Initial Value Theorem
- Final Value Theorem
Applying this to our problem
Bode Plot of the transfer function
Transfer Function
Bode Plot
==Break Points and Asymptotes==
Convolution
State Space
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Written By: Mark Bernet
Error Checked By: Greg Peterson