CE 573: Structural Dynamics
HW#3 Supplemental Problem
R
y
(x)
x
k
c
g
m
v = constant
Frame
Center of Mass
h
y(t)
Y(t)
Wheel
y
o
Given
:
A car can be (crudely) modeled as a single degree of freedom system having the entire car’s mass
m
lumped at the center of mass and connected to the frame (modeled as a rigid bar) by a linear
spring (stiffness =
k
, unstretched length =
l
o
) and a linear damper (damping constant =
c
). The
frame, in turn, is a fixed height
h
above the wheel, which rides over a rough road whose vertical
height above the fixed
x
axis is given by a known function
y
R
(x)
. The car starts at the location
x=0
at the initial time
t=0
(assume that
y
R
(x=0) = 0)
and it moves to the right with a constant
horizontal speed
v
. Let
Y(t)
be the height of the center of mass above the fixed
x
axis, let
y
o
be the
static equilibrium height of the center of mass at time
t=0
, and let
y(t)
be the height of the center
of mass above this static equilibrium position. Gravity acts downward as shown.
Required
:
(a) Determine the equation of motion for the car’s center of mass in terms of
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 Fall '05
 Whalen
 Mass, 30 meters, 30 m/s, 80 mm, 1430 kg

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