2.032 DYNAMICS
Fall 2004
Problem Set No. 1
Out
: Wednesday, September 15, 2004
Due
: Wednesday, September 22, 2004
at the beginning of class
Problem 1
(Doctoral Exam, 1999)
A pendulum is constructed by attaching a mass
m
to an extensionless string of fixed
length
l
. The upper end of the string is connected to the uppermost point of a vertical
fixed disk of radius
R
(
R < l/π
), as shown below. At
t
= 0 the mass hangs at rest at
the equilibrium position
θ
= 0, when it is given an initial velocity
v
0
along the horizontal.
Derive expressions for the two extreme deflections (in terms of
θ
) of the pendulum resulting
from this initial perturbation. Do
not
make a smallangle approximation.
g
v
0
R
m
θ
1
Courtesy of Prof. T. Akylas.
Used with permission.
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Problem 2
A point mass moves without friction on a horizontal plane. A massless inextensible string
is attached to the point mass and led through a hole (see figure below). At time =
t
0
the
mass moves along a circle with constant velocity
v
0
. We gradually pull the free end of the
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 Fall '04
 GeorgeHaller
 Mass, Prof. T. Akylas, Doctoral Exam

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