Physics 325, Fall 2010
Homework Assignment #5
Due Thursday 30 September at 11:15 am
1)
[15 points]
A mass is connected to four identical springs, each with spring constant
k
, as shown in the ﬁgure below. When the mass is at rest at (
x, y
) = (0
,
0), all four
springs are at their relaxed length. The system is then put into motion. At time
t
= 0, it
is observed that the position of the mass is (
x
0
, y
0
) and the velocity if the mass is (
v
0
x
, v
0
y
).
Note: 1. Ignore any eﬀects of gravity in this problem.
Note: 2. Assume the oscillation is much smaller than the length of the springs. In other
words, neglect the fact that the displacement of the springs in the xdirection are aﬀected
by the motion of the springs in the ydirection, and viceversa.
a) Determine
x
(
t
) and
y
(
t
).
For the next two parts, we modify the initial conditions to be as follows:
at time
t
= 0, it is observed that the position of the mass is (
x
0
, y
0
) and the velocity of
the mass is (0
, v
0
y
).
b) Is it possible to set
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 Fall '08
 Staff
 mechanics, Mass, Simple Harmonic Motion, Work, Damping ratio

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