View source for Laplace transforms: Critically Damped Motion

=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===


<math>m=\frac{8}{32}=\frac1 4 slugs<math>

<math>k=4