1. Consider the system in the following illustration.
   

   Sketch the Bode plot for the system.

2. By simply referring to the Bode plot, for each of the following inputs, determine y_ss(t) (the steady state response):
   1. r(t) = cos(0.1 t)
   2. r(t) = cos(t)
   3. r(t) = cos(10 t)
   4. r(t) = cos(50 t)
   5. r(t) = cos(100 t)
   6. r(t) = cos(1000 t)
3. Either write a computer program (C, C++ or FORTRAN) or use Simulink in Matlab to simulate this system. Compare the output, y_ss(t), for
   1. r(t) = cos(50 t) and
   2. r(t) = cos(0.1 t) + cos(50 t) + cos(1000 t).
   Explain the result.

Oysters are supposed to be the first course. Or terrapin. Then the soup, then the fish, then the mushrooms or asparagus, then the roast, then the frozen punch, then the game, then the salad, then the creamed dessert, then the frozen dessert, then the cheese, then the fruit, and then hungry guests can get into the candy and nuts.

--- Judith Martin (Miss Manners), August 21, 1996.