User talk:Gregory.peterson: Difference between revisions

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Created by Greg Peterson
Created by Greg Peterson


Checked by
Checked by Mark Bernet

Revision as of 15:44, 27 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...

Created by Greg Peterson

Checked by Mark Bernet