Uncertanty in a non-linear regression with least squares method

[VictorH]

Homework Statement

Ok, so I'm trying to fit a set of data (21000 points to be exact) to a sine function.

Homework Equations

Y = A*sin(ωt)

The Attempt at a Solution

I used NumPy to get the parameters A and ω with the least squares method. So far, so good. However, i appear to have reached an impass, this values don't have an uncertainty that accompanies them.

My question is: how do i propagate the error in the amplitude and the frecuency? In a quick web search I have not found any helpful inside in anything different of uncertainty of slopes in linear regressions. Can you recommend literature or websites that cover this topic? Bear in mind a freshman undergrad level of computer expertise and experimentation skill.

Thanks in advance

 

[maajdl]

You might get some inspiration by reading Numerical Recipes.

http://www.nr.com

http://apps.nrbook.com/c/index.html chap 15

Don't forget also to check for practical problems.
For example: aliasing, several frequencies can fit the same data, ...

 

[BvU]

Don't give a list of 21000 points, but:
Tell us a bit more about what was measured, and how.
Approximate frequency, sampling frequency,
Then write out what you did with numpy.
Did you get a $\chi^2$ out?

 

[VictorH]

Alright. So, i measured the movement of a vibrating table with a LVDT sensor, the approximate frecuency is around 30 Hz and a sampling frecuency of 1000 samples per second. Hopefully i can show it behaves like a harmonic oscillator. I looked at tha data, the graph is pretty nice and definitive to a sine function, so $\chi^2$ is a given, plus Python says so. I did least squares with Numpy (don't have the exact code at hand) and got some values for amplitude and frecuency.
Now, this numbers come very close of what i can see and measured in the lab. But, as in any experiment, this numbers mean nothing without uncertanties. My question is: how do i do error propagation in a non-linear regression using least squares?