The linearized equations of motion of the simple pendulum in Fig. 7.96 are +w0=u. (a) Write the equations of motion in state-space form. (b) Design an estimator (observer) that reconstructs the state of the pen- dulum given measurements of 6. Assume o = 5 rad/sec, and pick the estimator roots to be at s= -10 + 10j. (c) Write the transfer function of the estimator between the measured value of and the estimated value of 0. (d) Design a controller (that is, determine the state feedback gain K) so the roots of the closed-loop characteristic equation are at s = -44j.