13. What is the Laplace response of 4y + 3y = 1, y(0)=-1? 1 1 1 1 1 4 1 a) b) + c) d) s(4s+3) (4s+3) s(4s+3) (4s+3) s(4s+3) (4s+3) (4s+3) 14. For the system shown in Figure 2, z(t) is a displacement input, while x(t) and y(t) are variables. y shows the displacement at the node, and x shows the displacement of the mass. All the springs have the same value of stiffness, k. The damper coefficient is B. There is no damping between Mass and ground. For this system: a) Draw the free-body diagram, and show the equations of motion are: (10 Points); Mx + 2kx = ky + kz By + 2ky =kx y(t) x(t) k m k k B M W b) Using above equations, find the state space equations, and matrices. Consider the out to be the force in the spring between x and z (15 Points); c) Using above equations, find the transfer function Y(s) Z(s) (10 Points).