18.03 Problem Set 4 Fall 2009
Due in boxes in Room 2106, Friday Oct. 9 at 3:00 p.m.
You may and should discuss the problems with other students, but you must write solutions
entirely on your own. (The main reason for this requirement is that we enforce it so strictly on
exams.) Question Zero is required for your problem set to count.
0.
On the first page of your homework, list the individuals (other than recitation lead
ers, lecturer, and math department tutors) with whom you discussed the homework; and list
the sources (other than the class text, web site, and supplementary notes) that you consulted.
This will look like, “Consulted with Jane Doe; consulted text Birkhoff & Rota and web site
http://www.clepsydra.ch/
,” or “No consultation.”
1. (6 points) Find all the realvalued solutions of the differential equation
d
6
y
dx
6

y
= 0.
2. (12 points) The “spring and dashpot” system described on page 101 of the text satisfies the
differential equation
m
d
2
x
dt
2
+
c
dx
dt
+
kx
= 0
.
(Damped Spring)
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 Spring '09
 unknown
 Energy, web site, initial conditions, Damped Spring

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