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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

A wheel-and-tire assembly is being tested on a tire balancer. The wheel-and-tire assembly is slightly out of balance. If this wheel were on a car, the car could be very difficult to control.

What is known:

  • slider mass m1 = 20 kg
  • wheel and tire mass m2 = 25 kg
  • spring constant k = 7,000 N/m
  • damping constant c = 56 N s/m
  • eccentricity d = 1 cm
  • rotation speeds 90, 120, 150 rpm

   

Program Animation: 90 RPM
Click to view movie (31k)
  Question

 

What is the equation of motion for the platform on which the wheel is mounted?

   
  Approach

 
  • Determine the differential equation of motion.
  • Solve the differential equation for the homogeneous and particular parts.
  • Apply the initial conditions to the complete solution of the differential equation.
     

Program Animation: 150 RPM
Click to view movie (38k)
 
Program Animation: 120 RPM
Click to view movie (32k)