Simple Harmonic Motion

• Simple harmonic motion (SHM) is a special type of oscillation
• SHM occurs when a system has a stable equilibrium, and a restoring force which is linearly proportional to the distance from that equilibrium
• Amplitude controls the maximum displacement from equilibrium
• Angular frequency controls the rate of oscillation
• Phase angle specifies the conditions at time = 0
• The square of angular frequency is equal to the force constant of an oscillator, divided by its mass

• Viewgraph 1

• Viewgraph 2

  We can write this requirement for SHM in another way. Remember Newton's Second Law:

  

  If we replace the F in Hooke's Law with ma, we get

  

  or, if we write the derivative all by itself,

  

• Viewgraph 3

  We can examine the effect of each parameter by playing with a little application (click to activate)

  

• Viewgraph 4

• Viewgraph 5

  
  
    Q:  The vocal cords of an opera singer
        vibrate back and forth with a period
        of 0.8 milliseconds.
  
  
        What is the frequency of their oscillation?
  
  
        What is the angular frequency of their oscillation?
        
  
  

• Viewgraph 6

• Viewgraph 7

• Viewgraph 8

• Viewgraph 9

• Viewgraph 10