curve fitting - Matlab cftool giving a terrible fit for a simple graph

Question

I'm trying to do a fit on cftool for the movement of an oscillator in steady state. I've entered start points as accurately as I can, but Matlab keeps giving a terrible fit (R2 is negative.) This, though it's clear even visually that a better fit can be had.
By changing the upper and lower bounds, I can force the graph into a better fit. But it's still not 100%, Matlab keeps giving a negative R2, and when I take off the bounds, it returns to a worse fit. Current fit:

Data added upon request:

t1_w10_a5_ss:

8
8.05000000000000
8.10000000000000
8.15000000000000
8.20000000000000
8.25000000000000
8.30000000000000
8.35000000000000
8.40000000000000
8.45000000000000
8.50000000000000
8.55000000000000
8.60000000000000
8.65000000000000
8.70000000000000
8.75000000000000
8.80000000000000
8.85000000000000
8.90000000000000
8.95000000000000
9
9.05000000000000
9.10000000000000
9.15000000000000
9.20000000000000
9.25000000000000
9.30000000000000
9.35000000000000
9.40000000000000
9.45000000000000
9.50000000000000
9.55000000000000
9.60000000000000
9.65000000000000
9.70000000000000
9.75000000000000
9.80000000000000
9.85000000000000
9.90000000000000
9.95000000000000
10
10.0500000000000
10.1000000000000
10.1500000000000
10.2000000000000
10.2500000000000
10.3000000000000
10.3500000000000
10.4000000000000
10.4500000000000
10.5000000000000
10.5500000000000
10.6000000000000
10.6500000000000
10.7000000000000
10.7500000000000
10.8000000000000
10.8500000000000
10.9000000000000

x1_w10_a5_ss:
0.191254400000000
0.192137400000000
0.190920000000000
0.190923800000000
0.190562700000000
0.191785800000000
0.191260200000000
0.191621400000000
0.190396400000000
0.191092000000000
0.191080500000000
0.192133600000000
0.191264000000000
0.191273600000000
0.190388800000000
0.191780000000000
0.191776200000000
0.192137400000000
0.190916200000000
0.191269700000000
0.190736600000000
0.191785800000000
0.191260200000000
0.191617600000000
0.190742300000000
0.191269700000000
0.190738500000000
0.191615700000000
0.190914300000000
0.191443700000000
0.190736600000000
0.191785800000000
0.191260200000000
0.191617600000000
0.190738500000000
0.191611800000000
0.191256300000000
0.191961600000000
0.191088200000000
0.191443700000000
0.190740400000000
0.191441700000000
0.190912400000000
0.191615700000000
0.190914300000000
0.191443700000000
0.190742300000000
0.191271700000000
0.190568400000000
0.191269700000000
0.190740400000000
0.191443700000000
0.190742300000000
0.191271700000000
0.190566500000000
0.191439800000000
0.191084400000000
0.191789600000000
0.190916200000000

question from:https://stackoverflow.com/questions/65836518/matlab-cftool-giving-a-terrible-fit-for-a-simple-graph

Answer 1

I don't think that it is a problem of software. I observed a similar difficulty with another software and different method of fitting.

At first glance this look like white noice :

But there is another possible (and more physical) explanation. If the sampling frequency is too low compare to the oscillating frequency this is typically the kind of data that is commonly observed.

I suppose that you can roughly evaluate the frequency of oscillation at steady state by direct measurement (not from your data). What is the order of magnitude of the frequency of oscillation ? This is a very important piece of information to explain what is really the problem and to suggest what to do.