Problem 2 Consider the mechanical system shown below, where f(t) is the input force to the system. Z2 21 b 32 k f(t) m1 m2 The governing equations of motion for the system are given by: m1 + b(21-22) + kz = 0 m222 +b(2 1) = f(t) - (2) 1. Write the equations of motion in state-space form, where the state variables are [21, Z1, 2]. The output of the system is y = 21. 2. A linear state variable feedback controller is added to the system such that u = -Kx, where K denotes a column vector of feedback gains and x represents the state vector of the system. For m = m = 1kg, b = 1N-sec/m and k = 4N/m, determine the required feedback gains so that the poles of this closed-loop system are s = -2, 82 = -5, and 83 = -7. HINT: The determinant of a 3x3 matrix is given by: a det d e f = a h - b. +c.