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

 Index

Periodic motion concepts
 
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Large Amplitude Pendulum

An approximation for the large amplitude pendulum period
For L = cm and g = m/s2
when swung from angle θ0 =degrees:
s
s
s
for approximate periods

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. 		Index

Periodic motion concepts
 
HyperPhysics***** Mechanics R Nave
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