SINDy, Arbitrary Sine, Duffing system

[submerged-in-matrix]

I have used SINDy for predicting ME sensors output of a sinusoidal signal ,which is in linear case, a sinusoidal return (response). ME sensor can be modelled with a duffing equation. So I used SINDy to express the sinusoidal response of the sensor with a duffing system.
But If I use the same approach for fitting arbitrary sinusoidal datapoints, for example with np.sine(f), with the duffing equation , SINDy fails to predict. It makes sense to me as the data points did not come out of a duffing system. But If I use SINDy to fit datapoints generated by chossing random coefficients for the duffing equation and the displacement to be x = np.sine(t), it works.
I am not quite sure about how to argue more technically that datapoints generated by arbitrary np.sine(f) can't be modelled by a duffing system. Or am I wrong on that?
I would be helpful if I can get some expert opininon on that.
Best,
Sayeed