A 50 Hz, synchronous machine which has the inertia constant H = 5 s and transient reactance X = 0.2 p.u. is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance values are marked on the diagram on a common system base. Write the dynamic response of rotor angle and rotor speed to the step input x(t) = 10z(t) degrees when the generator is delivering real power of 0.6 p.u. at 0.8 power factor lagging to the infinite bus at voltage of 1 p.u. Solve the problem for the following two cases: (i) D = 0.15 X = 0.4 p.u. linel (ii) D = 0 X 0.2 .u. , %3D 0.1 .. - 0.4 .u. line2 E, = \E|46, V = 140