[<< wikibooks] Physics Course/Periodic Motion
== Periodic Motion ==
Periodic motion refers to any motion moving at a distance above and below the equilibrium position and this motion keeps repeat itself over a period of time. This type of motion is also called Oscillation .


== Examples ==
The moving up and down of a spring
The swinging side by side of a pendulum


== Analysis ==


=== The moving up and down of a spring ===
When apply a force on an object of mass m attach to a spring , the spring will move a distance y above and below the equilibrium point
The force acts on the object is

F = m aThe Restoring Force of spring is given by Hook's law as

Fs = - k yWhen The Net Force on the system is 0 then there is no movement

F - Fs = 0
m a = - k y
y = 
  
    
      
        
          
            
              m
              a
            
            k
          
        
      
    
    {\displaystyle {\frac {ma}{k}}}
  
a = - 
  
    
      
        
          
            k
            m
          
        
        y
      
    
    {\displaystyle {\frac {k}{m}}y}
  
v t = 
  
    
      
        
          
            k
            m
          
        
        y
      
    
    {\displaystyle {\frac {k}{m}}y}
  

  
    
      
        t
        =
        
          
            k
            m
          
        
        
          
            y
            v
          
        
      
    
    {\displaystyle t={\frac {k}{m}}{\frac {y}{v}}}
  


=== The swinging side by side of a pendulum ===