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PHY2061
R. D. Field
Department of Physics
chp36_5.doc
University of Florida
SHM Differential Equation
The general for of the
simple harmonic motion
(
SHM
) differential
equation is
dxt
dt
Cx t
2
2
0
()
+=
,
where
C
is a constant.
One way to solve this equation is to turn it into an
algebraic equation
by looking for a solution of the form
xt
Ae
at
=
.
Substituting this into the differential equation yields,
aA
e
CA
e
2
0
or
aC
2
=−
.
Case I (C > 0, oscillatory solution):
For positive
C
,
ai
Ci
=±
ω
, where
=
C
.
In this case
the most general solution of this
2
nd
order differential equation
can be
written in the following four ways:
x t
Be
A
t
B
t
A
t
A
t
it
co
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics, Simple Harmonic Motion

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