Laplace transforms: Critically Damped Motion: Difference between revisions
Jump to navigation
Jump to search
Mark.bernet (talk | contribs) |
Mark.bernet (talk | contribs) |
||
Line 110: | Line 110: | ||
<math>\text {This plot is done using the control toolbox in MatLab. }\,</math> |
<math>\text {This plot is done using the control toolbox in MatLab. }\,</math> |
||
[[Image:bode.jpg|700px|thumb|left|Fig (1)]] |
[[Image:bode.jpg|700px|thumb|left|Fig (1)]] |
||
==Break Points and Asymptotes== |
|||
==Break Points and Asymptotes== |
|||
<math>\text {A break point is defined by a place in the bode plot where a change occurs.}\,</math> |
<math>\text {A break point is defined by a place in the bode plot where a change occurs.}\,</math> |
||
Line 118: | Line 121: | ||
<math>\text {To find your break points you must start with a transfer function. }\,</math> |
<math>\text {To find your break points you must start with a transfer function. }\,</math> |
||
⚫ | |||
⚫ | |||
<math>\mathbf {X}(s)=-\frac{3}{(s+4)^2} </math><br /><br /> |
|||
<math>\text {A break point is located at any value where s = what is being added to it. }\,</math> |
|||
<math>\text {So for this transfer function its at s=4 (that is also the asymptotes location). }\,</math> |
|||
--- |
|||
Written By: Mark Bernet |
Written By: Mark Bernet |
Revision as of 16:12, 27 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
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
---
Written By: Mark Bernet
Error Checked By: Greg Peterson