PHY2061
R. D. Field
Department of Physics
chp36_4.doc
University of Florida
Simple Harmonic Motion
Hooke’s Law Spring:
For a
Hooke’s Law spring
the restoring force is linearly proportional to the
distance from equilibrium,
F
x
= kx
, where
k
is the spring constant.
Since,
F
x
= ma
x
we have
−
=
kx
m
d x
dt
2
2
or
d x
dt
k
m
x
2
2
0
+
=
,
where x = x(t).
General Form of 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 positive constant (
for the Hooke’s Law spring C=k/m
).
The
most general solution of this
2
nd
order differential equation
can be written
in the following four ways:
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 Spring '08
 FRY
 Physics, Derivative, Force, Simple Harmonic Motion, Hertz, Robert Hooke, Angular frequency

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