2.003 Quiz 1
This quiz has three problems. The numerical weighting of each problem is identical. The quiz
is closed-book, but you may reference one page of notes (both sides) that you have prepared.
Problem 1 (20 points) This problem concerns the second-order response shown below.
300
200
Amplitude
100
0
-100
-200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (sec.)
We also give an expanded picture of the response near t = 0:
300
200
Amplitude
100
0
-100
-200
0
0.05
0.1
Time (sec.)
a) What are the natural frequency and damping ratio of this response? (You can work
directly on the given time response plot and turn this in as part of your quiz work.)
b) Show us a mechanical system which will give this response, under the assumption that
the indicated response is position in millimeters. What are possible numerical values
of the system parameters and initial conditions that go with this response? Be sure to
show your reasoning.
1