AV_EX1

# AV_EX1 - (Present your solution in a symbolic form(b If for...

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Advanced Vibration Ex. 1 Submit Wed, Feb 2, 2011 Circle your final answers 1. The system shown in the figure below consists of a flexible pendulum of mass 1 m and spring k , of free length L , and a fixed length pendulum of length L and mass 2 m , as shown in the figure. Denote the length of the spring by ( ) t ρ , and assume that the mass of the spring is negligible. Numerical data: kg 10 1 = m , kg 15 2 = m , N/m 1000 = k , m 3 = L (a) Determine the equations of motion by both Newton’s and energy methods
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Unformatted text preview: (Present your solution in a symbolic form) (b) If for a particular instant rad 1 . 1 = θ , rad/s 3 . 1 = & , rad 15 . 2 = , rad/s 5 . 2 = & m 2 . 3 = , and m/s 5 − = & , what are 1 & & , 2 & & , and & & for this instant of time? (c) Linearize the equations of motion obtained in (a) (d) What are the poles of the linear system? What are its natural frequencies? 1 2 g O L 1 m 2 m...
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