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| <math>\mathbf {X}(s)=-\frac{4}{(s+2)^2} </math><br /><br /> | | <math>\mathbf {X}(s)=-\frac{4}{(s+2)^2} </math><br /><br /> |
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Revision as of 10:03, 23 October 2009
Using the Laplace Transform to solve a spring mass system that is critically damped
Problem Statement
An 98 Newton weight is attached to a spring with a spring constant k of 40 N/m.
The spring is stretched 4 m and rests at its equilibrium position.
It is then released from rest with an initial upward velocity of 2 m/s.
The system contains a damping force of 40 times the initial velocity.
Solution
Given
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
to be continued...