Equation of trendline for sinusoidal function.

[Chinmayee]

I have a set of experimental data that forms a sinusoidal function. I want excel to tell me the curve of best fit for these points and the equation for this curve. I have Excel 2010, and there is no option for a sinusoidal trendline. This is a sample of the data.

t x
0.00E+00 1.40E+02
1.67E-02 1.39E+02
3.34E-02 1.38E+02
5.01E-02 1.36E+02
6.67E-02 1.34E+02
8.34E-02 1.32E+02
1.00E-01 1.29E+02
1.17E-01 1.27E+02
1.33E-01 1.24E+02
1.50E-01 1.21E+02
1.67E-01 1.17E+02
1.84E-01 1.14E+02
2.00E-01 1.10E+02
2.17E-01 1.06E+02
2.34E-01 1.02E+02
2.50E-01 9.76E+01
2.67E-01 9.30E+01
2.84E-01 8.86E+01
3.00E-01 8.40E+01
3.17E-01 7.96E+01
3.34E-01 7.50E+01
3.50E-01 7.01E+01
3.67E-01 6.57E+01
3.84E-01 6.08E+01
4.00E-01 5.62E+01
4.17E-01 5.17E+01
4.34E-01 4.71E+01
4.50E-01 4.26E+01
4.67E-01 3.87E+01
4.84E-01 3.46E+01
5.01E-01 3.06E+01
5.17E-01 2.65E+01
5.34E-01 2.28E+01
5.51E-01 1.89E+01
5.67E-01 1.58E+01
5.84E-01 1.27E+01
6.01E-01 9.59E+00
6.17E-01 6.74E+00
6.34E-01 4.03E+00
6.51E-01 1.75E+00
6.67E-01 -5.12E-01
6.84E-01 -2.27E+00
7.01E-01 -4.15E+00
7.17E-01 -5.35E+00
7.34E-01 -6.81E+00
7.51E-01 -8.12E+00
7.67E-01 -8.88E+00
7.84E-01 -9.40E+00
8.01E-01 -9.81E+00
8.17E-01 -1.01E+01
8.34E-01 -1.01E+01
8.51E-01 -1.01E+01
8.68E-01 -9.33E+00
8.84E-01 -8.38E+00
9.01E-01 -7.43E+00
9.18E-01 -6.31E+00
9.34E-01 -5.07E+00
9.51E-01 -3.91E+00
9.68E-01 -2.21E+00
9.84E-01 -2.94E-01
1.00E+00 1.69E+00
1.02E+00 3.73E+00
1.03E+00 5.84E+00
1.05E+00 7.87E+00
1.07E+00 1.06E+01
1.08E+00 1.34E+01
1.10E+00 1.59E+01
1.12E+00 1.88E+01
1.13E+00 2.18E+01
1.15E+00 2.47E+01
1.17E+00 2.78E+01
1.18E+00 3.08E+01
1.20E+00 3.40E+01
1.22E+00 3.73E+01
1.23E+00 4.06E+01
1.25E+00 4.38E+01
1.27E+00 4.76E+01
1.28E+00 5.09E+01
1.30E+00 5.41E+01
1.32E+00 5.77E+01
1.33E+00 6.11E+01
1.35E+00 6.45E+01
1.37E+00 6.80E+01
1.38E+00 7.15E+01
1.40E+00 7.49E+01
1.42E+00 7.85E+01
1.43E+00 8.17E+01
1.45E+00 8.49E+01
1.47E+00 8.82E+01
1.48E+00 9.15E+01
1.50E+00 9.48E+01
1.52E+00 9.78E+01
1.53E+00 1.01E+02
1.55E+00 1.04E+02
1.57E+00 1.07E+02
1.58E+00 1.10E+02
1.60E+00 1.12E+02
1.62E+00 1.14E+02
1.63E+00 1.17E+02
1.65E+00 1.19E+02
1.67E+00 1.21E+02
1.69E+00 1.23E+02
1.70E+00 1.25E+02
1.72E+00 1.26E+02
1.74E+00 1.28E+02
1.75E+00 1.29E+02
1.77E+00 1.30E+02
1.79E+00 1.31E+02
1.80E+00 1.31E+02
1.82E+00 1.32E+02
1.84E+00 1.32E+02
1.85E+00 1.32E+02
1.87E+00 1.32E+02
1.89E+00 1.31E+02
1.90E+00 1.30E+02
1.92E+00 1.29E+02
1.94E+00 1.28E+02
1.95E+00 1.26E+02
1.97E+00 1.24E+02
1.99E+00 1.22E+02
2.00E+00 1.20E+02
2.02E+00 1.17E+02
2.04E+00 1.15E+02
2.05E+00 1.12E+02
2.07E+00 1.09E+02
2.09E+00 1.05E+02
2.10E+00 1.02E+02
2.12E+00 9.80E+01
2.14E+00 9.39E+01
2.15E+00 8.99E+01
2.17E+00 8.58E+01
2.19E+00 8.16E+01
2.20E+00 7.74E+01
2.22E+00 7.27E+01
2.24E+00 6.83E+01
2.25E+00 6.37E+01
2.27E+00 5.90E+01
2.29E+00 5.41E+01
2.30E+00 4.96E+01
2.32E+00 4.48E+01
2.34E+00 4.01E+01
2.35E+00 3.57E+01
2.37E+00 3.13E+01
2.39E+00 2.69E+01
2.40E+00 2.27E+01
2.42E+00 1.85E+01
2.44E+00 1.46E+01
2.45E+00 1.07E+01
2.47E+00 6.87E+00
2.49E+00 3.63E+00
2.50E+00 6.35E-01
2.52E+00 -2.57E+00
2.54E+00 -5.24E+00
2.55E+00 -7.62E+00
2.57E+00 -9.79E+00
2.59E+00 -1.20E+01
2.60E+00 -1.39E+01
2.62E+00 -1.53E+01
2.64E+00 -1.63E+01
2.65E+00 -1.73E+01
2.67E+00 -1.78E+01
2.69E+00 -1.82E+01
2.70E+00 -1.82E+01
2.72E+00 -1.79E+01
2.74E+00 -1.72E+01
2.75E+00 -1.63E+01
2.77E+00 -1.52E+01
2.79E+00 -1.35E+01
2.80E+00 -1.18E+01
2.82E+00 -1.02E+01
2.84E+00 -7.78E+00
2.85E+00 -5.36E+00
2.87E+00 -2.86E+00
2.89E+00 -7.18E-03
2.90E+00 2.99E+00
2.92E+00 6.31E+00
2.94E+00 9.81E+00
2.95E+00 1.35E+01
2.97E+00 1.73E+01
2.99E+00 2.13E+01
3.00E+00 2.54E+01
3.02E+00 2.96E+01
3.04E+00 3.37E+01
3.05E+00 3.78E+01
3.07E+00 4.18E+01
3.09E+00 4.60E+01
3.10E+00 5.05E+01
3.12E+00 5.47E+01
3.14E+00 5.88E+01
3.15E+00 6.29E+01
3.17E+00 6.69E+01
3.19E+00 7.10E+01
3.20E+00 7.48E+01
3.22E+00 7.88E+01
3.24E+00 8.27E+01
3.25E+00 8.64E+01
3.27E+00 9.00E+01
3.29E+00 9.30E+01
3.30E+00 9.65E+01
3.32E+00 9.96E+01
3.34E+00 1.03E+02
3.35E+00 1.05E+02
3.37E+00 1.08E+02
3.39E+00 1.11E+02
3.40E+00 1.13E+02
3.42E+00 1.15E+02
3.44E+00 1.17E+02
3.45E+00 1.19E+02
3.47E+00 1.20E+02
3.49E+00 1.22E+02
3.50E+00 1.23E+02
3.52E+00 1.24E+02
3.54E+00 1.25E+02
3.55E+00 1.25E+02
3.57E+00 1.26E+02
3.59E+00 1.26E+02
3.60E+00 1.26E+02
3.62E+00 1.26E+02
3.64E+00 1.25E+02
3.65E+00 1.24E+02
3.67E+00 1.24E+02
3.69E+00 1.23E+02


Thanks for any help, I appreciate it!

[MrShorty]

Do you want to use a simple sin function (with amplitude, period, and phase shift as your regression parameters), or do you need more of a Fourier transform regression?

A simple sine function can be fit using non-linear regression techniques programmed into Excel. Provide some initial guesses for your function, compute the estimated curve and "objective function" (if you want to use a standard least squares objective function, you can use =SUMXMY2() https://support.office.com/en-us/art...4-e2ecee23b299 ). Then call Solver and tell it to minimize (or maximize, if appropriate) your objective function by changing the regression parameters of the function.

If you want a more robust Fourier transform, I would point you to this thread, with a link to a spreadsheet built for Fourier transform analysis: http://www.excelforum.com/excel-char...dal-curve.html