(a) Define a state vector X and write a state-space representation of the system. Please note: the pulling force is an input to the system and should not be regarded as a state. (Q2a.i) Select the correct state vector X in Figure 9. /LMS Input: One integer) (Q2a.ii) Two of the state-space equations are 13 = f3(1, X2, . . .) + 93(12) F(t) cosx] CA = fA(X1, X2, . . . ) + 94(12) F(t) cosx1 Find the values of (a) 93(7/3) and (b) g4(7/3). [LMS Input: Two signed numbers accurate to 3 significant figures/ For parts (b), (c) and (d). Assume that the pulling force is F(t) = (2+ v3) g N (i.e., constant). (b) Find all of the distinct equilibrium states for the system when qi E (-7, 7] and q2 E (-7, 7]. Draw a schematic diagram of the system for each of the equilibriums. (Q2b.i) For an equilibrium X = let h(X) = 12 (X1 + 212 + 313). Order the equilibriums such that . . . h ( X 1 )