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<math>\dot{x}(0)=-3</math> |
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<math>\dot{x}(0)=-3</math> |
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<math>\text {Standard equation: }\,</math> |
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<math>\text {Standard equation: }\,</math> |
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<math>m\frac{d^2x}{dt^2}+C\frac{dx}{dt}+khx=0</math> |
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===Solving the problem=== |
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===Solving the problem=== |
Revision as of 19:14, 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
Solving the problem