Laplace transforms: Critically Damped Motion: Difference between revisions

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<math>\text {k=4}\,</math>
<math>\text {k=4}\,</math>


<math>\text {Damping constant (c)=2}\,</math>
<math>\text {Damping constant C=2}\,</math>

Therefore the equation representing this system is

<math>\text {\frac{dy}{dx}}\,</math>

Revision as of 17:16, 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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