Midterm One EECS 461, Fall 2018

issued electronically: 12:00 PM Thursday November 8, 2018 due electronically: 8:00PM Thursday November 8, 2018 Name:..........SOLUTIONS.................. • Four problems, weighted equally. • Reasons should be stated clearly and concisely to receive maximum credit. • Open notes from EECS 461, Fall 2018 only. 1.2.3.4............ ........... ........... ........... Sign the Honor Code: “I have neither given nor received aid on this exam, nor have I concealed any violation of the honor code.” Signature:................................................................... 1 1. Consider the problem of balancing a stick in the palm of your hand, as shown in Figure 1. If we regard the position of your hand, u, as an input and the horizontal position of the end of the stick, y as the output, and we further assume that the angle θ is small, then the system is described by the second order differential equation g g ÿ − y = u, (1) L L where g = 10 m/sec2 is the acceleration due to gravity and L is the length of the stick.