Determine the location x of the centroid C of the shaded area that is part of a circle having a radius r. y x C r _ x a a Prob. 971

Notes Taken for EMT on March 28, 2016 First Order System with a Harmonic input Recall, for a step input, we had F(t) = 0 @ t = 0 A F(t) = a 0 @ t > 0 For a Harmonic Input to the 1 order system, we have F(t) = 0 @ t =0 A F(t) = sin(ωt ) for t > 0 a 0 amplitude frequency The solution for harmonic input is A −t x(f) = a0 −1 τ 2 sin[ωt−tan ωt )]+Ce √ 1+(ωt) a 1 again, τ = a0 The Phase Shift is defined as −1 Φ(ω) = tan (ωt) (ϕ is in radians) ϕ(ω) The steady state response lags by time delay ωt = & ω is the frequency of the si