ME 240
–
Fall 2011
Computer Assignment 1
(Due in class October 14, 2011)
Consider a mass
m
, hanging from a massless pendulum rod
starting from rest at the position
Θ
= 0
. The
mass moves through a viscous fluid, which generates a damping force proportional
to the mass’s
velocity and opposing its motion (
D

= c

v

)
. Let
R
denote the length of the pendulum rod,
D
denote
the drag force imposed onto the mass,
T
denote the tension force in the pendulum rod, and
P
denote a
tangential control force obeying
P =
0.5mgcos(Θ)
, and where
g
is the acceleration due to gravity as
shown in the figure.
Figure 1: Mass
m
attached to a pendulum rod of length
R
1.
Draw a freebody diagram of the mass in the position shown in Figure 1. Clearly show the unit
vectors in your freebody diagram and all forces that act on the mass.
2.
Using
∑
⃑
⃑
, show that the equation of motion in the tangential direction is
̇
̈
3.
After you have obtained this equation of motion, it can be reduced to
̈
̇
P
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4.
Assume the values of the constants to be
R =
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 Fall '09
 PERKINS
 Physics, Force, Mass, pendulum rod

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