Assigned 12-Feb.                                                                                                Due 24-Feb.

This assignment will explore a situation similar to that in Example 10-5 in your text. There are two
 situations which we want to consider and compare:

Undamped Case - Resonance Excitation

The standard form of the differential equation for forced motion at resonance is:

               (a1)

or

              (a2)

where

                                 (a3)

The homogeneous solution to (a2) is

(b)

where A and B are arbitrary constants. The particular solution to (a2) is

      (c)

Suppose and the initial conditions are: .

1a) Determine the analytical solution to (a) subject to the above initial conditions (for the given numerical values).

1b) Write a program which will plot the solution using MATLAB © from t =0 until t = 1 sec.

Damped Case - Resonance Excitation

The standard form of the differential equation for forced motion at resonance is:

              (A1)

or

       (A2)

where

                                        (A3)

and

                                        (A4)

The homogeneous solution to (A2) is

  (B1)

where

                    (B2)

where A and B are arbitrary constants. The particular solution to (A2) is

                            (C)

Suppose and the initial conditions are:
.

2a) Determine the analytical solution to (A) subject to the above initial conditions (for the given numerical values).

2b) Write a program which will plot the solution using MATLAB © from t =0 until t = 1 sec.

3a) Plot the results from 2b) on top of 1b).
 
 

3b) On your plot, sketch the envelopes of the two solutions. Describe the envelopes in words. What is the ultimate
       steady-state amplitude in the damped case? What about the undamped case? Will it ever reach steady-state?
 
 

4) Discuss any similarities in the two plots as well as any differences.
 
 

5) Turn in the work for your analytical solutions, the plot, your discussion, and a printout of your MATLAB code.