ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 4
Due: June 28, 2010
Q1.
A massless disc of radius
R
has an embedded particle of mass
m
at a distance
R/2
from the
center.
The disc is released from rest in the position shown and rolls without slipping down the
fixed inclined plane.
Find:
(a) the equation of motion of the particle in terms of the angle
and its time derivatives;
(b)
as a function of
. This is really integration of the equation of motion starting
with the initial condition given above in the statement.
Hint: It is easier to do in terms of
the energy conservation principle for the particle.
(Problem 310 in the text).
Q2.
Initially the spring has its unstretched length
0
l
and the particle has a velocity
0
v
in the
direction shown.
In the motion that follows, the spring stretches to a maximum length of
0
4
/3
l
.
Assuming no gravity (motion in horizontal plane), find the spring stiffness
k
as a function of
m
,
0
l
, and
0
v
.
(Problem 315 in the text).
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 Fall '10
 BAJAJ
 Particle, smooth horizontal table, differential equation models, appropriate initial conditions, energy conservation principle

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