Simple Pendulum

Monday, 11 June 2018

11:24 AM

If a pendulum undergoes periodic motion for angles smaller than 10 degrees, it can be considered to move under simple harmonic motion

 

Such that

 

 Equating

 

 for


 

 

 

Also,

So therefore:

And so,

 

The period and frequency of a simple pendulum depend only on the length of the string and the acceleration due to gravity.

The mass of the bob is independent, and doesn't affect the  motion of the pendulum.

All simple pendula that are of equal length and are at the same location oscillate with the same frequency.

 

 

 

Machine generated alternative text: • The tangential motion is then described by: —m g sin 0 mas=m sin s=LO Small angle approximation When 0 is small, a simple pendulum's motion can be modeled as simple harmonic motion about the equilibrium position 0 d20 radian —mg 0 SHM! tangential radial Frictionless pivot cord Bob mg sin 0 Gravitational force mg cos 0 mg

 

Machine generated alternative text: SHM>Simple pendulum... • Compare What we just derived: General equation of motion for SHM in terms of the angular frequency: d20 There is no dependence on the mass of the bob! Angular frequency of an oscillating pendulum Acceleration due to gravity Length of cord Period

 

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