In the movie \"Enchanted\", Robert and Nancy are in an on-off relationship. The

Question

In the movie "Enchanted", Robert and Nancy are in an on-off relationship. The more Nancy likes Robert, the less he likes her. The more Robert likes Nancy, the more she likes him. If r(t) is the amount that Robert likes Nancy at time t, and n(t) is the amount that Nancy likes Robert at time t, then r'(t) = -n(t) and n'(t) = r(t). Make a sketch of r(t) and n(t) on the same set of axes, if Robert is initially completely committed to Nancy (r(0) = 1) and Nancy is initially completely indifferent to Robert (n(0) = 0). Explain how you produced your graphs, without referring to any formula.

Explanation / Answer

since r'(t)=-n(t) and n'(t)=r(t) r'(t) is also equal to n''(t) so n''(t)=-n(t) this implies n(t)=Asin(wt) this implies r(t)=Acos(wt) from the given conditions r(0)=0 we have , r(0)=A=1 r(t)=cos(wt) n(t)=sin(wt) hence graph of r(t) will be a cosine curve with amplitude 1 and graph of n(t) will be sine curve of amplitude 1. pls rate it

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