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<math>\text {Which appears to mean the system will be below equilibrium after a long time. }\,</math> |
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<math>\text {Which appears to mean the system will be below equilibrium after a long time. }\,</math> |
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==Bode Plot of the transfer function== |
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===Transfer Function=== |
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<math>\mathbf {X}(s)=-\frac{3}{(s+4)^2} </math><br /><br /> |
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===Bode Plot=== |
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<math>\text {This plot is done using the blank in MatLab. }\,</math> |
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---- |
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Written by: Mark Bernet Checked by: |
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
Written by: Mark Bernet Checked by: