[Bonus problem (20 points) - You can use Matlab in this problem] Consider a system consisting of a motor driving two masses that are connected by a torsional spring, as shown in the following diagram: ΦΙ Motor @1 J 92 @2 J2 This system can represent a motor with a flexible shaft that drives a load. Assuming that the motor delivers a torque that is proportional to the current I, the dynamics of the system can be described by the equations J101 + c(102) + k(01-02) = kl J202+ c(21) + k(02-01) = Td, where Ta is a disturbance torque on the second mass and the parameter values are J₁ = 10/9, J2 = 10, c = 0.1, k = 1, k₁ = 1. (a) Determine a state-space description with u = (I, Ta) and y = (01, 02). (b) Verify that the system is controllable both from I and from Td. Recall that I is the control input and Ta is a disturbance input that cannot be used for actually controlling the system. (c) Investigate the stability of the system. (d) Design a state feedback that places the eigenvalues at -2, -1, -1±i. (e) Simulate the responses of the closed-loop system to perturbations in the initial conditions and to a step change in the disturbance torque on the second rotor.