Laplace transforms: Critically Damped Motion: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
Line 23: Line 23:
<math>\dot{x}(0)=-3</math>
<math>\dot{x}(0)=-3</math>


<math>\text {Standard equation: }\,</math>
<math>\text {Standard equation: }\,</math>
<math>m\frac{d^2x}{dt^2}+C\frac{dx}{dt}+khx=0</math>



===Solving the problem===
===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