Second order ODE application question

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SUMMARY

This discussion focuses on the application of second order ordinary differential equations (ODEs) in mass spring problems, specifically using a stiffness matrix defined as K = [ -(k1+k2), k2; k2, -(k2+k3)]. The participants analyze a stiffness matrix derived from given parameters (m1=m2=1; k1=0, k2=2, k3=0), resulting in a matrix with a determinant of zero. The conversation highlights confusion regarding the relationship between degrees of freedom and parameters, emphasizing the need for a solid understanding of linear algebra to navigate these concepts effectively.

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  • Understanding of second order ordinary differential equations (ODEs)
  • Familiarity with stiffness matrices in mechanical systems
  • Basic knowledge of linear algebra, particularly matrix operations
  • Concept of degrees of freedom in mechanical systems
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  • Study the properties of stiffness matrices in mechanical systems
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Students and professionals in mechanical engineering, applied mathematics, and physics who are working with mass spring systems and second order ODEs, particularly those seeking to strengthen their understanding of linear algebra in this context.

cue928
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We are doing mass spring problems that stem from second order ODE's. I think my lack of linear algebra is hurting me once again in this section so any help would be greatly appreciated.
We are using a stiffness matrix of K = [ -(k1+k2), k2 (row 2) k2, -(k2+k3)]
Our first problem has the following values: m1=m2=1; k1=0, k2=2, k3=0
Setting up the stiffness matrix I got the following:
-2 2
2 -2
So this is my first stopping point: I thought you were supposed to then take the inverse of that but can you do that with a matrix that has a determinant of zero?
 
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hi cue928! :smile:

not really my subject, so I'm going to risk asking what could be a really dumb question :redface: …

if there's only two degrees of freedom, how come there's three parameters? :confused:

(and your general formula doesn't have rows summing to 0 …

maybe these are just the top triangle of a 3x3 matrix?)​
 
I don't know how to answer that. Since there is a zero value for two of them, maybe that has something to do with it? I honestly don't know.
 

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