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==
=Using the Laplace Transform to solve a spring mass system that is critically damped=


===Problem Statement===
==Problem Statement==
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.
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.


===Solution===
==Solution==

Revision as of 17:54, 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.

Solution