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I am trying to calculate 2nd derivative from my data, but somehow I have strange feeling about it, any thoughts?
Well, "strange feelings" are poorly defined, so I don't really know what you mean by that. Your x array is spaced equally, so all you need to get is dt and the differentiate Y twice. Of course a second derivative is typicilly significantly more noisy than the original data, so you might want to add some filtering too (not shown).