Curve fit second order differential equation from data

[jstoph]

Is there any way to find a curve from least squares or anything like that to find coefficients of a second-order differential equation by inputting a data set?

Thanks in advance

[jstoph]

something like this would be excellent:

[altenbach]

You can fit anything you want. What have you tried so far?

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[jstoph]

My apologies - I haven't tried anything yet, I am very new to LabView. I have a set of data that I wish to fit rather than solve a differential equation and am not sure how to proceed. 

relating force to a variable (displacement, velocity, or acceleration) and unknown constants:

[altenbach]

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@jstoph wrote:

My apologies - I haven't tried anything yet, I am very new to LabView.

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I don't think there is anything specific to LabVIEW. How would you solve it in any other programming envoronment?

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@jstoph wrote:
I have a set of data that I wish to fit rather than solve a differential equation and am not sure how to proceed. 

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In order to fit, you need two things:

• data (F(x) measured) as a function of an independent variable (e.g. x). Do you have data?
• A model function that can calculate F(x) (simulate the data!) based on x and a set of fitting parameters.

For some problems, there is a direct linear algebra solution available (e.g. linear or polynomial fit). For more complicated problems, an iterative procedure (e.g. Levenberg Marquardt) needs to be used, where, given an initial guess for the fitting parameters, the fitting algorithm will adjust them in way to best match the data to the model. In your case.

In your case, the differential equation needs to be solved for each iteration. Do you know the initial conditions for the differential equation or is this also to be fit??

[jstoph]

I have about 7,000 KB of data on an excel spreadsheet. 

I am not sure what you mean by initial conditions - the time we start "recording" data can be adjusted if it makes curve fitting easier. Mostly need to figure out said function for an object dropping in freefall, then striking an object which causes a damped oscillation.

[altenbach]

Pleas explain what you mean by "fit"?

Of course there are analytical solutions for damped oscillations. What parameters are you interested in?

[jstoph]

I really am searching for coefficients which would be used to write a function that can best describe my data.

[altenbach]

Can you attach some data?

Some analytical solution can be found here, of course. The solution will depend on the initial condition, for example if the mass is resting at the equilibrium, nothing interesting will probably happen.

[jstoph]

I can't due to the sensitive nature of the project. It recorded about 20,000 data points in ~20 seconds. It recorded time, force, and two accelerations (the two accelerations were very similar but not exactly the same.)