Ch 10. Vibrations dy Multimedia Engineering Dynamics Free Vibs. Undamped Free Vibs. Damped Forced Vibration Energy Method
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll

 DYNAMICS - CASE STUDY Spring Constant = 5,000 lb/ft Animation Click to view movie (367k) Spring Constant = 10,000 lb/ft Animation Click to view movie (331k) 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 Problem Parameters 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.