Laplace transforms: Critically Damped Motion: Difference between revisions
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<math>\text {k=4}\,</math> |
<math>\text {k=4}\,</math> |
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<math>\text {Damping constant |
<math>\text {Damping constant C=2}\,</math> |
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Therefore the equation representing this system is |
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<math>\text {\frac{dy}{dx}}\,</math> |
Revision as of 18:16, 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.
Solution
Things we know
Therefore the equation representing this system is
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