"If an elderly but distinguished scientist says that something is possible he is almost certainly right, but if he says that it is impossible he is very probably wrong"
Arthur C. Clarke

• Oscillatory motion is Simple Harmonic Motion if the magnitude of the restoring force (F_R ) is linearly proportional to the magnitude of the displacement (x) from equilibrium.  This relationship is known as Hooke's Law after the seventeenth century English physicist Robert Hooke .

  F_R  =  - k x

  where k is the constant of proportionality, commonly called the "spring" constant, even for SHM not involving springs. The negative sign indicates that the restoring force and the displacement are measured in opposite directions.
   

• The time taken to complete one oscillation is called the PERIOD (T) and is given by the expression,

  
  

  where m is the mass of the oscillating object.
   

• The FREQUENCY(f) of the motion is the number of oscillations which take place in one second,

  f = 1/T

  Frequency is measured in Hertz    (Hz),  1 Hz = 1 s^-1
   

• The AMPLITUDE  (A) of the motion is defined as the maximum value of the displacement.

 
• Frequency (and period) is independent of the amplitude of the oscillations.

 
• When an object undergoes SHM the total energy of the system is made up of kinetic and potential energies the relative amounts of which oscillate with the frequency of the motion.

For example, in the case of a mass on a spring, kinetic energy is converted to and from ELASTIC potential energy,





 
• If  displacement in SHM is plotted as a function of time the result is the "familiar" sine (or cosine) wave.

 

 


Note that in this diagram the displacement is labelled 'y' rather than 'x'.


 

   Supplementary Problems 

"The prime minister held a meeting with the cabinet today. He also spoke to the bookcase and argued with the chest of drawers."

Ronnie Barker


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu