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
d x t
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
x t
Ae
at
( )
=
.
Substituting this into the differential equation yields,
a Ae
CAe
at
at
2
0
+
=
or
a
C
2
= −
.
Case I (C > 0, oscillatory solution):
For positive
C
,
a
i
C
i
= ±
= ±
ω
, where
ω
=
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
Ae
Be
x t
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 Spring '08
 FRY
 Physics, Derivative, Simple Harmonic Motion, Algebraic geometry

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