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1.053J/2.003J Dynamics and Control I
Fall 2006
Exam 2
20
th
November, 2006
Important Notes:
1.
You are allowed to use two lettersize sheets (twosides) of notes.
2.
There are three problems on the exam. You have 80 minutes
to solve them.
3.
Each problem carries equal weight: 20 points.
Cite as: Sanjay Sarma, Nicholas Makris, Yahya ModarresSadeghi, and Peter So, course materials for 2.003J/1.053J
Dynamics and Control I, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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Problem 1 (20 Points)
Figure 1
Two blocks of masses
m
1
and
m
2
are connected by a spring with a spring constant
k
and
are free to slide on a horizontal surface as shown in Figure 1(a).
The drag between each
mass and the surface can be modeled as viscous damping with a dashpot constant
c
as
shown in Figure 1(b).
Initially the masses are at rest and the spring is unstretched.
At
t
= 0
, a horizontal force
F
is applied to mass
m
2
.
Derive the equation(s) of motion for this
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 Spring '05
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