An inverted pendulum on a cart is 53 cm long. The cart suddenly moves by 2.4 mm. Use gravitational acceleration of 9.81 m/s2. (a) We know from the inverted pendulum analysis that using proportional feedback for the pendulum, the system response is oscillatory. If K = 114.3 cm/rad, obtain the response of the pendulum (i. e., et)), its amplitude, and the period of oscillation. (b) Obtain the response function., et), for the same pendulum if we use proportional-plus-integral feedback with K = 114.3 cm/radian and K2 = 668.1 cm/s-radian.