|
|
Line 112: |
Line 112: |
|
[[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 118: |
|
<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>\text {Transfer function }\,</math> |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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