Show how the function y = e^(-x) sin x could represent damped oscillation.

Question

a) Determine the local extreme for a sequence of wavelengths.
b) Show that the local maxima represent exponential decay.

Answer 1

(a) there is a local extreme every time sinx = cosx: x = π/4 + kπ

(b) since the maxima occur when sinx=1, the envelope of these maxima is the curve y=e^-x.