High-speed rail pantograph. Problem 21 in Chapter 1 discusses active control of a pantograph mechanism for high-speed rail systems. The diagram for the pantograph and catenary coupling is shown in Figure P2.39(a). Assume the simplified model shown in Figure P2.39(6), where the catenary is represented by the spring, Kavc

a. Find the transfer function, G\{s) = Ycal(s)/ ^up(s), where ycat(f) is the catenary displacement and /up(r) is the upward force applied to the pantograph under active control.

b. Find the transfer function G2(s) = Yh(s)/Fup(s), where yh(t) is the pantograph head displacement.

c. Find the transfer function, G(s) = (Yt,(s)- Ycat(s))/Fap(s).