Ch 2 HW Solutions - Part2

Ch 2 HW Solutions - Part2 - J = mR 2 = 2 . The equation of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
10 CHAPTER 2 SDOF VIBRATION: AN INTRODUCTION By the energy method, we substitute the kinetic and potential energies into the principle of the conservation of energy. T = 1 2 I _ 2 ; V = mgl cos T + V = 1 2 I _ 2 mgl cos = const : Di/erentiating the total energy with respect to time, I _ + mgl sin _ = 0 _ ( I + mgL sin ) = 0 : Since _ 6 = 0 , we can divide it out of the expression, leaving us with the equation of motion I + mgL sin = 0 : Fig.2.33 Take the moment about the vertical axis through the center of the disk to obtain + X M G = J = J where J is the mass polar moment of inertia. For a solid disk
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: J = mR 2 = 2 . The equation of motion is J & & + K& = 0 ; and the natural frequency is then ! n = p K=J: Using the energy approach, we &rst &nd the kinetic and potential energies, and then apply the principle of energy conservation T + V = constant. T = 1 2 J _ & 2 , V = 1 2 K& 2 T + V = 1 2 J _ & 2 + 1 2 K& 2 = const: Di/erentiating the total energy and dividing the expression by _ &; we obtain the same equation of motion J & & + K& = 0 ....
View Full Document

Ask a homework question - tutors are online