Ch 10. Vibrations 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 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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