Write down the solution u(t, ) to the initial value problem (a) A non-resonant forcing function at frequency (b) A resonant forcing

Write down the solution u(t, η) to the initial value problem

(a) A non-resonant forcing function at frequency η ‰  ω
(b) A resonant forcing function at frequency η = ω.
(c) Show that, as η †’ ω, the limit of the non- resonant solution equals the resonant solution. Conclude that the solution u(t, η) depends continuously on the frequency η even though its mathematical formula changes significantly at resonance.

dr2