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Simple Pendulum

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Introduction
Problems
Answers

      
Introduction

A simple pendulum consist of a bob suspended from the end of a lightweight cord.  The cord cannot stretch and the mass of the cord must be small compared to the mass of the bob.  With negligible friction, the motion resembles SHM.  

The bob oscillates along the arc of a circle with with equal amplitudes on either side of the equilibrium position.  It has maximum velocity at the equilibrium position and zero velocity at the amplitudes.  

Displacement along arc x = L

The restoring force is F = - mg sin

The negative sign illustrates that the restoring force is in the opposite direction.

At small angles, less than 15o    sin

F = - mg

Substituting in x = L   we get
     

            mg
F  =  -  ----- x
             L		 For small displacements, the motion is essentially simple harmonic.  This is true because this equation fits Hooke's law, F = - kx, where the effective force constant is k = mg/L.

The period of a simple pendulum can be found be substituting k = mg/L into

   giving

   

   
     must be small 
   

Since f  =  1/T

   

Observe that the period is independent of the amplitude as long as the amplitude is kept small, less than 15o.  

It is also independent of the mass.

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Problems

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Answers

 

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