Consider a driven undamped spring/mass system described by the initial-value problem d'x + w*x = F, sin yt, x(0) = 0, x'(0) = 0. dr

Consider a driven undamped spring/mass system described by the initial-value problem

(a) For n = 2, discuss why there is a single frequency γ₁/2π at which the system is in pure resonance.

(b) For n = 3, discuss why there are two frequencies γ₁/2π and γ₂/2π at which the system is in pure resonance.

(c) Suppose ω = 1 and F₀ = 1. Use a numerical solver to obtain the graph of the solution of the initial value problem for n = 2 and γ = γ₁ in part (a). Obtain the graph of the solution of the initial-value problem for n = 3 corresponding, in turn, to γ = γ₁ and γ = γ₂ in part (b).

d'x + w*x = F, sin" yt, x(0) = 0, x'(0) = 0. dr %3D %3D