Suppose we have a mechanical system with the following model: \bar{v}+6 \dot{v}+13 v=13 n where y is the output of the system and u is the input of the system.

Initial conditions are y(0)and y(0). ) Based on the given model, generate the transfer function Y(s)/U(s). (b) What are the poles and zeros of the transfer function? (c) If the input u(t) is a unit step, find the output y(t) when y(0) = 0 and ý(0) = 0. (d) Write down an expression for the free response with initial conditions y(0) =1 and ÿ(0)=0 (e) Is this system stable? Please explain.