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SUMMARY
The goal of Chapter 14 has been to understand systems that oscillate with simple harmonic motion.
General Principles
Dynamics
SHM occurs when a
linear restoring force
acts to return
a system to an equilibrium position.
Horizontal spring
Vertical spring
The origin is at the equilibrium
position
Pendulum
v5
Å
g
L
T
5
2
p
Å
L
g
(
F
net
)
t
52
1
mg
L
2
s
v5
Å
k
m
T
5
2
p
Å
m
k
(
F
net
)
y
52
ky
D
L
5
mg
/
k
.
(
F
net
)
x
52
kx
Energy
If there is
no friction
or
dissipation, kinetic and
potential energy are
alternately transformed
into each other, but the
total mechanical energy
is conserved.
In a
damped system,
the
energy decays exponentially
where is the
time constant
.
t
E
5
E
0
e
2
t
/
t
5
1
2
kA
2
5
1
2
m
(
v
max
)
2
E
5
1
2
mv
x
2
1
1
2
kx
2
E
5
K
1
U
Important Concepts
Simple harmonic motion (SHM)
is a sinusoidal oscillation
with period
T
and amplitude
A
.
Frequency
Angular frequency
Position
Velocity
with maximum speed
Acceleration
a
x
52v
2
x
v
max
5v
A
v
x
(
t
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This note was uploaded on 09/26/2010 for the course PHYS 021 taught by Professor Dick during the Spring '08 term at GWU.
 Spring '08
 Dick
 Physics, Force, Simple Harmonic Motion

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