3/31/2011
1
Physics 1C
Lecture 12B
"Imagine if we taught baseball the way we teach science.
Undergraduates might be allowed to reproduce famous
historic baseball plays.
But only in graduate school would
they, at last, actually get to play a game."
Alison Gopnik
SHM: Mathematical Model
Equations of motion for SHM:
Remember, simple harmonic
motion is
not
uniformly
accelerated motion
SHM: Mathematical Model
The maximum values of velocity and acceleration for an
object in SHM:
The velocity is 90
o
out of
phase with the displacement
and the acceleration is 180
o
out of phase with the
displacement
SHM
–
Example 1
Initial conditions at
t = 0
are:
x
(0)=
A
and
v
(0) = 0
This means
f
= 0
The acceleration reaches
extremes of
w
2
A
The velocity reaches
extremes of
w
A
SHM
–
Example 2
Initial conditions at
t = 0
are:
x
(0)= 0
and
v
(0) =
V
i
This means
f
=

p
/2
The graph is shifted one
quarter cycle to the right
compared to the graph of
x
(0) =
A
MassSpring Energy
Let’s assume a spring
mass system is moving on
a frictionless surface
This is an isolated system, therefore the total
energy of the system is constant
The kinetic energy is:
KE
= 1/2
mv
2
= 1/2
m
w
2
A
2
sin
2
(
w
t
+
f
)
•
The elastic potential energy is:
PE
= 1/2
kx
2
= 1/2
kA
2
cos
2
(
w
t
+
f
)
•
The total energy is:
KE
+
PE
= 1/2
kA
2
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