Imagine you find a model of Sin[t] from t=0 to t=Pi/4 and discover that f=t-t^3/6 seems adequate.
Then imagine you plot that function from t=0 to t=8*Pi and wonder why it goes off to infinity.
I suspect there must be a theorem that says extrapolating far beyond the range of almost any numerical model must result in the function going off to infinity.
I believe this is what is happening with your two versions.
In your first you find a model from t=0 to t=5760 and plot over the same.
In your second you find a model from t=0 to t=1440 and plot over t=0 to t=5760
