Laplace transforms: Critically Damped Motion: Difference between revisions
Jump to navigation
Jump to search
Mark.bernet (talk | contribs) |
Mark.bernet (talk | contribs) |
||
Line 17: | Line 17: | ||
<math>\text {k=4}\,</math> |
<math>\text {k=4}\,</math> |
||
<math>\text {C= |
<math>\text {C=2}\,</math> |
||
<math>\text {x(0)=0}\,</math> |
<math>\text {x(0)=0}\,</math> |
Revision as of 16:54, 18 November 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
Apply the Initial and Final Value Theorems to find the initial and final values
- Initial Value Theorem
- Final Value Theorem
Applying this to our problem
Bode Plot of the transfer function
Transfer Function
Bode Plot
==Break Points and Asymptotes==
Convolution
State Space
---
Written By: Mark Bernet
Error Checked By: Greg Peterson