Pendulum-displacement-amplitude of vibration

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SUMMARY

The amplitude of vibration for a pendulum swinging through a total of 42 degrees is definitively 21 degrees. This value represents the maximum displacement from the equilibrium position, calculated by halving the total swing angle. The small angle approximation applies, as the amplitude is below 45 degrees, allowing the angular position to be modeled by the equation: angle = 21 cos (2*pi/T * t) [degrees], where T is the oscillation period.

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Homework Statement


A child on a playground swings through a total of 42 degrees. If the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?
(Disregard frictional forces acting on the swing)

The Attempt at a Solution


I know amplitude is the maximum displacement, but I am not sure how to get the answer with the degrees.
Would it just be 42 degrees?
 
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Just came to my mind: usually amplitude of a sinusoidal function is taken from equilibrium position to maximum displacement, so it would be 21 degrees. If the small angle approximation holds (usually you can assume it holds for amplitudes below 45 degrees) the angular position of the boy could be described by:

angle = 21 cos (2*pi/T * t) [degrees]

where T is the oscillation period.

kcmccraw said:

Homework Statement


A child on a playground swings through a total of 42 degrees. If the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?
(Disregard frictional forces acting on the swing)




The Attempt at a Solution


I know amplitude is the maximum displacement, but I am not sure how to get the answer with the degrees.
Would it just be 42 degrees?
 
yeaaaa it's 21! i got it right on the test a few days ago i had to guess though :( :D thanks.
 

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