Laplace transforms: Under-damped Mass-Spring System on an Incline: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 5: Line 5:


===Problem Statement===
===Problem Statement===
Find the equation of motion for the mass in the system subjected to the forces shown in the Free Body Diagram (FBD).
Find the equation of motion for the mass in the system subjected to the forces shown in the Free Body Diagram (FBD). The inclined surface is coated in SAE 30 oil.


[[Image:Setup.jpg|300px]]
[[Image:Setup.jpg|300px]]


===Initial Conditions and Values===
===Initial Conditions and Values===
A is the area of the box in contact with the surface; g is the gravitational acceleration field constant; b<sub>t</sub> is the thickness of the fluid covering the surface
* A is the area of the box in contact with the surface
* g is the gravitational acceleration field constant
* b<sub>t</sub> is the thickness of the fluid covering the inclined surface
* &mu; is the viscosity constant of the fluid;
* m is the mass of the box
* k is the spring constant

<Math>
A = 1/2 m^2

</Math>



===Equations of Equilibrium===
===Equations of Equilibrium===

Revision as of 22:58, 25 October 2009

Brandon.plubell 05:44, 26 October 2009 (UTC)

Under-Damped Mass-Spring System on an Incline

Part 1 - Use Laplace Transformations

Problem Statement

Find the equation of motion for the mass in the system subjected to the forces shown in the Free Body Diagram (FBD). The inclined surface is coated in SAE 30 oil.

Setup.jpg

Initial Conditions and Values

  • A is the area of the box in contact with the surface
  • g is the gravitational acceleration field constant
  • bt is the thickness of the fluid covering the inclined surface
  • μ is the viscosity constant of the fluid;
  • m is the mass of the box
  • k is the spring constant


Equations of Equilibrium

FBD.jpg

Laplace Transform

Inverse Laplace Transform

Equation of Motion

Part 2 - Final and Initial Value Theorems

Initial Value Theorem

Final Value Theorem

Part 3 - Bode Plot

Part 4 - Breakpoints and Asymptotes on Bode Plot

Retrieved from "http:///class-wiki/index.php?title=Laplace_transforms:_Under-damped_Mass-Spring_System_on_an_Incline&oldid=5374"