Second order ODE application question

In summary, the conversation discussed mass spring problems and the use of a stiffness matrix. The speaker mentioned their lack of linear algebra knowledge and requested help. The stiffness matrix was given as K = [-(k1+k2), k2; k2, -(k2+k3)]. The first problem had specific values for m1, m2, k1, k2, and k3, resulting in a stiffness matrix of -2, 2; 2, -2. The speaker was unsure about taking the inverse of this matrix due to its determinant being zero. A question was also raised about the number of parameters and the formula not having rows summing to zero.
  • #1
cue928
130
0
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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  • #2
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?)​
 
  • #3
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.
 

1. What is a second order ODE?

A second order ODE (ordinary differential equation) is a mathematical equation that describes the relationship between a function and its derivatives. It involves the second derivative of the function, hence the term "second order". It is commonly used in physics and engineering to model various phenomena.

2. What are some common applications of second order ODEs?

Second order ODEs are used in many areas of science and engineering, such as mechanics, electromagnetics, fluid dynamics, and heat transfer. They can be used to model the motion of a pendulum, the behavior of a spring, the flow of electricity, and many other physical systems.

3. How do I solve a second order ODE?

There are various methods for solving second order ODEs, depending on the specific equation and initial conditions. Some common techniques include separation of variables, substitution, and using power series. It is important to have a solid understanding of calculus and differential equations in order to effectively solve these equations.

4. Can second order ODEs be solved numerically?

Yes, second order ODEs can be solved numerically using methods such as Euler's method, Runge-Kutta methods, or finite difference methods. These techniques involve approximating the solution at discrete points and using iterative calculations to find the overall solution.

5. What are the real-world implications of solving a second order ODE?

Solving a second order ODE can have practical applications in fields such as engineering, physics, and economics. By using these equations, scientists and engineers can model and predict the behavior of complex systems, leading to advancements in technology and understanding of the natural world.

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