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DYNAMICS - CASE STUDY

    Introduction


Problem Graphic
 

A marble in a spherical bowl oscillates with an apparently simple harmonic motion, however for large oscillations this motion becomes quite difficult to describe.

What is known:

  • marble radius r = 0.04 ft
  • marble mass m = 0.003 slugs
  • bowl radius R = 1 ft
     


Problem Diagram

  Question

 

What is the frequency of the marble's motion in the bowl for small oscillations?

   
  Approach

 
  • Determine the kinetic energy and potential energy for the marble.
  • Find the equation of motion by setting the time derivative of the total energy equal to zero.
  • Solve the equation of motion.
     
   
 
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