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A damped mass-spring oscillator is subjected to a forcing F=F_0 cos〖(ω_d t)〗. The steady-state solution is given by x=A cos〖(ω_d t-δ)〗, where A=A(ω_d )=(F_0/m)/√((ω_0^2-ω_d^2 )^2+(γω_d )^2 ) and tanδ=(γω_d)/(ω_0^2-ω_d^2 ). The symbols have the usual meanings. A sketch of the variation of amplitude versus driving frequency is shown in Figure 1: Figure 1: Variation of amplitude with driving frequency Explain why the amplitude is F_0/k when the driving frequency is zero and the type of forcing the system is subjected to. Show that the frequency at which the amplitude attains a maximum is given by ω_m=√(ω_0^2-γ^2/2) and that the maximum amplitude is given by A=A_0 Q/[1-1/(4Q^2 )]^(1/2) where Q is the quality factor and A_0=F_0/k
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