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Solve 2nd order differential equation?

Posted 2 years ago
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I have been trying to Solve a system of 8 second order differential equations converted to a matrix representation. Its has been running for 7 days and is still running. Should I wait for it solve or should I abort as it could be due to some error. I will attach the screen captures here for reference. I am in need of the general solution. Please help me out.Image shows the Matrices of the coefficients of the second order differential equation to be solved

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I would recommend solving it numerically with NDsolve. Is there a reason you need an analytical solution? I doubt that you will ever get one given the complexity of the equations. Numerically your equations will be easy to solve.

Thanks for your suggestion Neil. I thought if I had the general solution, I could use it for finding the solutions for different Symbolic constant values. It has been 8 days now and suddenly Mathematica states that the memory is not sufficient and that the Mathematica kernel has shutdown. Is going for the numerical solution the only option?Image shows the error message thrown by mathematica

Numerically this solution would be straightforward. Your equations appear to come from a model of a physical system --probably a series of masses, springs and dampers -- am I correct?

If this is the case, I would recommend looking at Wolfram's SystemModeler. It is a much easier way to work with physical systems and it integrates well with Mathematica. You could arrange the blocks in a physical way, change constants from SystemModeler or Mathematica, get an animation of your system for visualization, and even run sensitivity analysis on your constants (see which ones have the biggest effect on some output).

Yes, It is a system of masses, springs and dampers. I was not aware of the Wolfram's SystemModeler option. Would certainly give it a try and post the updates related to it. Thanks for your kind suggestion.

Note to Moderator: This Thread should be added to the SystemModeler Group.

I put together a quick example to get you started. I used the translational blocks -- they do not animate. If you want an animating example I can quickly put one together for you. The force is turned on at 2 seconds. By modifying this model you should be able to do whatever you want. Note-- I made the second mass always two times the first mass (but you can change this to a number or an equation). The attached file is the full model for SystemModeler. Here is a picture of what I did:

enter image description here

The simulation results:

enter image description here

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