Laplace transforms: Critically Damped Motion: Difference between revisions
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=Using the Laplace Transform to solve a spring mass system that is critically damped= |
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==Problem Statement== |
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An 8 pound weight is attached to a spring with a spring constant k of 4 lb/ft. |
An 8 pound weight is attached to a spring with a spring constant k of 4 lb/ft. |
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The spring is stretched 2 ft and rests at its equilibrium position. |
The spring is stretched 2 ft and rests at its equilibrium position. |
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The system contains a damping force of 2 times the initial velocity. |
The system contains a damping force of 2 times the initial velocity. |
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==Solution== |
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Revision as of 16:54, 22 October 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.