The motion control of a lightweight hospital transport vehicle can be represented by a system of two masses, where m1 - m2 = 1 and k1= k2 = 1 [21]. (a) Determine the state vector differential equation, (b) Find the roots of the characteristic equation, (c) We wish to stabilize the system by letting u = -kx1,, where u is the force on the lower mass, and x, is one of the state variables. Select an appropriate state variable x1. (d) Choose a value for the gain k and sketch the root locus as k varies.