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DYNAMICS - CASE STUDY


Problem Parameters

  Introduction

 

Designers are testing a new idea for an amusement ride. The design is basically a large platform that is on vertical sliders and connected to a spring. The system is subjected to an initial displacement then released. If the designers are not careful, the ride may be to dangerous to use.

What is known:

  • mass m = 1,000 slugs
  • spring constant k = 5,000 or 10,000 lb/ft
  • initial displacement y(0) = -20 ft
  • initial velocity y(0) = 0 ft/s
   
    Question

 

What is the maximum acceleration the occupants will undergo during the ride?

   
  Approach

 
  • Model the ride as a spring-mass system.
  • Displace the system from its equilibrium position.
  • Draw a free-body diagram.
  • Determine the differential equation of motion using F = ma.
  • Solve the equation of motion for the displacement.
  • Differentiate with respect to time twice to get the acceleration equation.
     
   
 
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