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
2
2
0.40 m s
and
rad
s
0.127 m
12.7 cm
2.0 s
rad s
v
v
A
A
T
π
π
ω
ω
π
ω
π
=
=
=
=
⇒
=
=
=
=
(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
π
⎡
⎤
=
=
⎣
⎦
=
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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 ZHOU
 Energy, Kinetic Energy, Simple Harmonic Motion, 0.02 m

Click to edit the document details