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to return the block to its equilibrium position (
x
= 0). Since the acceleration
a
=
d
2
x
/
d
2
,
Newton’s second law yields
=.
2
2
12
m
dx
dt
kx kx
−−
Substituting
x
=
x
m
cos(
ω
t
+
φ
) and simplifying, we find
=
+
2
kk
m
where
is in radians per unit time. Since there are 2
π
radians in a cycle, and frequency
f
measures cycles per second, we obtain
=
2
=
1
2
f
m
ππ
+
.
The single springs each acting alone would produce simple harmonic motions of
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Acceleration, Force

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