For the physical system, (1) Draw free-body diagrams and write the modeling equations (2)Obtain the Laplace Transform of these modeling equations. All initial conditions are assumed non-zero. Do not attempt to solve.

a b Let A = and let k be a scalar. Find a formula that relates det(kA) to k and det(A). c d Find det(A). det(A) = (Simplify your answer.) Find det(kA). det(kA) = | (Simplify your answer.) Use the preceding steps to find a formula for det(kA). Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer.) A. det(kA) = • det(A) + B. det(kA) = + det(A) Oc. det(kA) = |- det(A) O D. det(kA) = • det(A)

The "Yaw Damper System" provides airplane stabilization about the yaw axis. The Yaw Damper minimizes dutch roll during flight by providing rudder displacement proportional to, and opposing, the yaw rate of the airplane. Transfer function of the yaw damper is taken as: 4.833 yaw rate rudder angle (s+0.551)(s+0.1 ±0.541*i) (s+0.616)(s +0.058+ i)(s+0.007) a) Give a brief knowledge about yaw dampers. b) Draw and interpret "root-locus" graphic of this transfer function. c) Draw and interpret the yaw rate distribution according to time.