I have a taylor expansion models as below. Can someone help me to understand the following plot? In the plot for A0 model, the plot is shifted towards right, which I understand. But with A1 model, I expected that the result will improve due to more terms in expansion, but the A1 model is overestimating. I could not understand, why this happens.
f(x) is a envelop of response of mass spring system. And I was trying to evaluate f(x-a).
zoom of the peak:
$$f(t-a) \approx f(t) :--- A0 $$
$$f(t-a) \approx f(t)-a*f'(t) :--- A1 $$
$$f(t-a) \approx f(t)-a*f'(t) + \frac{a^2}{2}f''(t) :--- A2 $$
