LT with IC=O of (1), (2) and (3) (ms + k) Y(s) = ka(s) kX(s)+ k Y(s) = (3k+k2) a(s) (ms + k) X(s) = F(s) + ka(s) (1) into (2) (1) (2') (3') le X(s\ + k ka G(s) = (3k+kla(s) mx s+kd 2 8(s) = k (mas+kd) X(s) (3k+kla (m s + k) - k a (3')-> (ms + k) X(s) = F(s) + ka k (mas +hd) X(s) - G(s) = X(s) = F(SY (3k+b)a (my s+k)- (3k+k) (ma s+x) - k (ms + k) [(3k + kd) (mys k) - k] - k (mys e) that eliminates lxssl@w* DVA condition: Numerater of G(jw*) = 0 -> 3km w = 2 3k - m2 = 13 2 69.7681 N/m answers are given, please explain highleted portions. (d and e). show with detailed steps how theta(s) was simplified and G(s). also please explain in part e how k was found. thanks! Problem 1 (60): Consider the suspension system shown in Fig. (a) that is initially at equilibrium. The bar AOB is massless and rigid and is free to rotate about the fixed point O. A sinusoid force f(t) is 50 kg, k = 500 N/m. applied at the mass m. The values of the system parameters are m = fit) = Psi: w -r a 0 Fig (! a TIT ri 2 a) Determine the transfer function of the system G(s) = b) What is the resonance frequency vibration x(t) at this frequency" c) Sketch the Bode diagram of G(s). X(s) F(s) of the system and what is the steady-state amplitude of the To attenuate the vibration of the mass m we suspend a dynamic vibration absorber of mass ma= 10 kg as shown in Fig (b). I... t) = Psi wi. 121 E 77777 c) e) Determine the transfer function G(s) = *(s) of the coupled system. F(s) Determine the value of the stiffness k, that will result in the elimination of the steady-state vibrations x(1) of the mass m at the frequency w. f) What are the resonant frequencies of the coupled system in Fig (b)? g) Sketch the Bode diagram of the transfer function G(s) coupled-system in d)