Pendulum-displacement-amplitude of vibration

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In summary, the child on the playground swings through a total of 42 degrees and the displacement is equal on each side of the equilibrium position. The amplitude of the vibration can be calculated as 21 degrees, taking into account the small angle approximation and the oscillation period.
  • #1
kcmccraw
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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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  • #2
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?
 
  • #3
yeaaaa it's 21! i got it right on the test a few days ago i had to guess though :( :D thanks.
 

Related to Pendulum-displacement-amplitude of vibration

What is the definition of pendulum displacement amplitude of vibration?

Pendulum displacement amplitude of vibration refers to the maximum displacement of a pendulum from its rest position as it swings back and forth.

How is pendulum displacement amplitude of vibration related to the length of the pendulum?

The pendulum displacement amplitude of vibration is directly proportional to the length of the pendulum. This means that as the length of the pendulum increases, the displacement amplitude also increases.

What factors can affect the pendulum displacement amplitude of vibration?

The pendulum displacement amplitude of vibration can be affected by factors such as the mass of the pendulum, the angle at which it is released, and the strength of the gravitational force.

What is the formula for calculating pendulum displacement amplitude of vibration?

The formula for calculating pendulum displacement amplitude of vibration is A = L * sin(theta), where A is the amplitude, L is the length of the pendulum, and theta is the angle at which it is released.

How does pendulum displacement amplitude of vibration affect the period of a pendulum?

The pendulum displacement amplitude of vibration has no effect on the period of a pendulum. The period is only affected by the length of the pendulum and the strength of the gravitational force.

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