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14.4.
Model:
The airtrack glider attached to a spring is in simple harmonic motion.
Visualize:
The position of the glider can be represented as
x
(
t
)
=
A
cos
ω
t
.
Solve:
The glider is pulled to the right and released from rest at
0 s
t
=
. It then oscillates with a period
and a maximum speed
2.0 s
T
=
max
40 cm s
0.40 m s
v
==
.
(a)
max
max
22
0
.
4
0
m
s
and
rad s
0.127 m
12.7 cm
2.0 s
rad s
v
vA
A
T
ππ
ωω
π
ωπ
=
=
⇒
=
=
(b)
The glider’s position at
t
=
0.25 s is
()
(
)
0.25 s
0.127 m cos
rad s
0.25 s
0.090 m
9.0 cm
x
⎡⎤
⎣⎦
=
COS wave
The graph shows the position x of an oscillating object as a function of time. The
equation of the graph is
,
where A is the amplitude,
ω
is the angular frequency, and
φ
is a phase constant. The
quantities M, T and N are measurements to be used in your answers.
What is A in the equation? A=M
What is
ω
in the equation? 2
π
/T
What is
φ
in the equation? 2
π
N /T , looked at Figure, when t = N, x (N) = M, that is M = M cos(2
π
/T*(N)+
φ
)
→
cos(2
π
/T*(N)+
φ
) =1, 2
π
/T*(N)+
φ
=0, so that
φ
= 2
π
N /T
14.14.
Model:
The oscillating mass is in simple harmonic motion.
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This note was uploaded on 04/18/2010 for the course PHYS ? taught by Professor Zhou during the Spring '10 term at Georgia State University, Atlanta.
 Spring '10
 ZHOU

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