Laplace transforms: Critically Damped Motion: Difference between revisions

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<math>\frac{d^2x}{dt^2}+8\frac{dx}{dt}+16x=0</math>
<math>\frac{d^2x}{dt^2}+8\frac{dx}{dt}+16x=0</math>



<math>\text {Now that we have the equation written in standard form we need to send
<math>\text {Now that we have the equation written in standard form we need to send}\,</math>
it through the Laplace Transform}\,</math>
<math>\text {through the Laplace Transform}\,</math>

Revision as of 18:26, 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