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be the coordinate as a function of time for particle 1 and
=
2
2
+
6
2
x
At
T
cos
ππ
F
H
G
I
K
J
be the coordinate as a function of time for particle 2. Here
T
is the period. Note that since
the range of the motion is
A
, the amplitudes are both
A
/2. The arguments of the cosine
functions are in radians. Particle 1 is at one end of its path (
x
1
=
A
/2) when
t
= 0. Particle
2 is at
A
/2 when 2
π
t
/
T
+
π
/6 = 0 or
t
= –
T
/12. That is, particle 1 lags particle 2 by one
twelfth a period. We want the coordinates of the particles 0.50 s later; that is, at
t
= 0.50 s,
1
20
.
5
0
s
=c
o
s
=0
.
2
5
2
1.5 s
A
x
A
π
×
§·
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 Spring '08
 Any
 Physics

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