CEE511 – Structural Dynamics
Winter Semester 20052006
Homework #2
(Due January 30, 2006 – Slip Under My Door)
Modeling Discrete Parameter Systems  Equations of Motion
1.
Chopra Problem 1.12
2.
Chopra Problem 1.19
3.
Derive the equations of motion for the following pendulum system.
The rod length is
L
, and
its mass density is uniform across its surface area.
Assume
b << L
(so make small angle
approximations).
Mass density is
ρ
but total mass of rod is
m
.
Note: the term “rod” does not
imply a simple rod.
a.
Derive the equation of motion of the system:
b.
Simplify the equation of motion assuming the displacement angle,
θ
, is small
c.
Determine the natural frequency of the rod system based on the simplified
equation of motion in part (b).
b
L
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The same rod is taken and now rotated about a new pivot point (as shown
below).
Find the natural frequency of the new rod system configuration.
Again,
make small angle approximations to find the rod’s equation of motion.
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 Spring '06
 Lynch
 Natural Frequency, wood beam, small angle approximations, new pivot point

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