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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
dx
dt
2
2
or
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
dxt
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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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, Force, Simple Harmonic Motion

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