14.64.
Model:
Assume the smallangle approximation.
Visualize:
Solve:
The tension in the two strings pulls downward at angle
.
θ
Thus Newton’s second law is
2
sin
y
y
F
T
ma
θ
= −
=
∑
From the geometry of the figure we can see that
2
2
sin
y
L
y
θ
=
+
If the oscillation is small, then
y
L
±
and we can approximate
sin
/
.
y L
θ
≈
Since
y
/
L
is
tan
,
θ
this
approximation is equivalent to the smallangle approximation sin
tan
θ
θ
≈
if
1 rad.
θ
±
With this
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 Fall '09
 geller
 Simple Harmonic Motion, 2 L, 1 rad, Smallangle approximation, smallangle approximation sinθ

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