1 Chap 04, Problem 7]. We have four timepieces whose performance is described as follows: The wall clock loses two minutes in an hour. The table clock gets two minutes ahead of the wall clock in an hour. The alarm clock falls two minutes behind the table clock in an hour. The last piece, the wristwatch, gets two minutes ahead of the alarm clock in an hour. At noon all four timepieces were set correctly. Let x equal the wall clock reading, 22 be the table clock reading, x3 the alarm clock reading, and 24 the wristwatch reading, and consider noon as the starting time (i.e., k = = 0). (a) Write the dynamic equations corresponding to the four given statements about performance. Directly translate into the form (5 points) Ex (k + 1) = Cx (k)+c (b) Convert the system to the standard form x(k + 1) = Ax(k) + b [Hint : (I B)-1 = I+B+B? + + Bk + ... whenever B is such that the series converges.] (5 points) (c) Find the state-transition matrix (k). (5 points) (d) Find a simple general formula for x(k). What time will the wristwatch show at 7:00 p.m. (i.e., at k = 7)? (5 points) 1 Chap 04, Problem 7]. We have four timepieces whose performance is described as follows: The wall clock loses two minutes in an hour. The table clock gets two minutes ahead of the wall clock in an hour. The alarm clock falls two minutes behind the table clock in an hour. The last piece, the wristwatch, gets two minutes ahead of the alarm clock in an hour. At noon all four timepieces were set correctly. Let x equal the wall clock reading, 22 be the table clock reading, x3 the alarm clock reading, and 24 the wristwatch reading, and consider noon as the starting time (i.e., k = = 0). (a) Write the dynamic equations corresponding to the four given statements about performance. Directly translate into the form (5 points) Ex (k + 1) = Cx (k)+c (b) Convert the system to the standard form x(k + 1) = Ax(k) + b [Hint : (I B)-1 = I+B+B? + + Bk + ... whenever B is such that the series converges.] (5 points) (c) Find the state-transition matrix (k). (5 points) (d) Find a simple general formula for x(k). What time will the wristwatch show at 7:00 p.m. (i.e., at k = 7)? (5 points)