Modelling a spring system with damping force and external forces

Thread starter sss1
Start date Sep 30, 2023
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Damping Spring System

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The discussion centers on modeling a spring system that includes damping and external forces, with one participant suggesting the system is critically damped based on a graph. They request examples of systems exhibiting damping without external forces and with external forces, expressing confusion over the term "external force" in a Newtonian context. Additionally, a question arises regarding the equation 10y'' + 9y" + 2y' = -2e^(-t/2) and why it differs from 19y'' + 2y' = -2e^(-t/2), along with a query about the distinction between y'' and y". The conversation highlights the complexities of damping in spring systems and the interpretation of forces in mathematical modeling. Understanding these concepts is essential for accurately analyzing dynamic systems.

Sep 30, 2023

sss1

Homework Statement: I know for a system with no external forces there are conditions for being underdamping, overdamping and critically damped. Is there also such conditions for systems having external forces acting on them also? Specifically, for the example 10y''+9y"+2y'=-2e^(-t/2) with conditions y(0)=0 and y'(0)=0, is the system critically damped?

Relevant Equations: 10y''+9y"+2y'=-2e^(-t/2)

I think its critically damped by looking at the graph of the solution.

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Sep 30, 2023

kuruman

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Can you give an example of a system with no external forces that exhibits damping and a system with external forces that also exhibits damping? I do not understand your use of "external force" at least not in the Newtonian sense.

Also, if 10y''+9y"+2y'=-2e^(-t/2), why not 19y''+ 2y'=-2e^(-t/2)? Is there a real difference between y'' and y"?

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