Explain simple pendulum, Physics

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Explain Simple Pendulum

The most familiar example of a pendulum is a person on a swing.  The person will swing back and forth if pushed or pulled from where the swing naturally hangs (its equilibrium position). The distance and force along the path of the swing are:

1837_Simple Pendulum.png

θ = ω t
ω = 2Π / T
d = Lsin ω t
F = m g sin θ = m at = m ω2 L sin ωt

When θ is a small angle, it is approximately equal to sin θ, and the pendulum follows simple harmonic motion. This gives a relationship between T (period in seconds) and L (length of the pendulum in meters) and g (acceleration due to gravity, 9.8 m/s2 ).

T = 2Π (L/g) ½

The most interesting aspect of this relationship is that  it does not depend on m, the mass of the pendulum!! 
The only way to change the period of a swing is to change its length or ship it to a different planet having a different value for g.

 


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