When a spring with natural frequency λ/ 2 πis driven with a sinusoidal force sin(ωt) with ω≠λ, it oscillates according to y(t)=(1)/(λ^2-ω^2)(λsin(ωt)-ωsin(λt)) Let y0(t)=limω→λ y(t) (a) Use L'Hôpital's Rule to determine y0(t) (b) Show that y0(t) ceases to be periodic and that its amplitude |y0(t)| tends to ∞ as t →∞( the system is said to be in resonance; eventually, the spring is stretched beyond its limits). (c) [R 5 Plot y(t) for λ=1 and ω=0.8,0.9,0.99, and
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