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Oscillations
If a loaded spring is pulled down and
released, the system moves up and
own about its equilibrium position.
This up and down
motion of the load is
called an
oscillation
.
The rest position of the load is
called its
equilibrium
position
When the load is pulled down to
a
lower extreme
,
the work done
in stretching the spring becomes
potential energy of the spring
which pulls the load back to the
equilibrium position.
1
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View Full Document The kinetic energy at
the equilibrium
position does work
compressing the
spring so that the
load moves to the
upper extreme
,
compressing the
spring.
equilibrium
Lower extreme
The compressed
spring has
potential energy
and it does work
pushing the load
back to the
equilibrium
position giving it
kinetic energy.
The spring has potential energy when the load is
at either extreme. The load is at rest at the
extremes and its kinetic energy is zero.
2
At the equilibrium position, the
potential energy of the spring is
zero. The load has maximum
kinetic energy at this position.
The amount of
stretch of the spring
from its equilibrium
position is called
the
displacement (y)
of the load.
The maximum displacement of the load
from the equilibrium position is called the
amplitude (A)
of the oscillation.
Equilibrium
Upper Extreme
Lower Extreme
A
U = 0, K
max
K = 0, U
max
K = 0, U
max
3
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View Full Document As the load oscillates between
the two extremes, its
displacement
y
changes
reaching a maximum at the
upper extreme
(
y = A
)
and a
minimum at the lower extreme
(
y = A
).
We will now obtain an
equation for the
displacement y as a
function of time.
Equilibrium
Upper Extreme
Lower Extreme
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMe
A
A
4
A
θ
B
C
BC
is a diameter
of the circle.
O
A perpendicular
drawn from
Q
meets
BC
at
O
.
O
is called the projection
of
Q
onto
BC
If the center of the circle is the origin, when the
object is at
P
,
the projection
O
is at the origin.
When the object is at
Q
,
the projection
O
moves up.
y
,
the distance it moves up is called
the
displacement
of the projection.
y
P
Q
Consider an object moving around a circle of radius
A
.
At t = 0, the
object is at P.
A little while later,
the object is at the
point
Q
so that the
radius rotates
through an angle
θ
.
5
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View Full Document A
θ
B
C
O
y
P
Q
When the object is at B, the projection
O
also is at B.
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.
 Fall '10
 George
 Physics

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