Large Amplitude Pendulum
The usual solution for the
simple pendulum
depends upon the
approximation
which gives the equation for the
angular acceleration
but for angles for which that approximation does not hold, one must deal with the more complicated equation
The detailed solution leads to an elliptic integral. That solution can be approximated by a series, for which the first three terms are
Calculation
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Large Amplitude Pendulum
An approximation for the
large amplitude pendulum
period
For
L =
cm and
g =
m/s
^{2}
when swung from angle
θ
_{0}
=
degrees:
s
s
s
for approximate period
s
This period deviates from the
simple pendulum
period by
percent. You can explore numbers to convince yourself that the error in pendulum period is less than one percent for angular amplitudes less than 22 degrees.
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Periodic motion concepts
HyperPhysics
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Mechanics
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