16.61
Prof. J. P. How
Prof. J. Deyst
Handout #4
March 6, 2003
Due:
March 13, 2003
16.61 Homework Assignment #4
1. Consider the spring pendulum analyzed before. The arm attached to the rotating shaft
has length
d
= 0
.
8m, as shown in the figure.
The shaft is rotating with a constant
angular velocity Ω = 0
.
4 rad/sec, but the pendulum is free to change length (
L
) and
swing (
θ
). Given that the spring constant is
k
and the mass of point P is
m
, find the
equations of motion for this system. Note that gravity acts.
Pay special attention to Frame selection and FARM.
2. A pendulum of mass
m
and length
l
is in a uniform gravitational field. The support
point is moving in the vertical direction with a displacement
d
(
t
), which is a
known
function of time (Both
˙
d
(
t
) and
¨
d
(
t
) are known as well).
(a) Use Newton’s method to solve for the equations of motion of this system. What
frames would be useful to select to solve this problem? Assume small angles.
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 Spring '03
 EarlMurman
 Kinetic Energy, Mass, Pay special attention

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