Explanation Given information: A section of uniform pipe is suspended from two vertical cables attached at A and B. The pipe is given a small rotation about centroidal axis OO’ and released. Calculations: From the figure shown above: A A ' = B B ' = a 2 θ m = l α m α m = a 2 l θ m At Position 1: K i n e t i c e n e r g y : T 1 = 0 P o t e n t i a l e n e r g y : V 1 = m g y c = m g l ( 1 − cos α ) f o r s m a l l a n g l e s ( 1 − cos α m = 2 sin α m 2 ≈ α m 2 2 = a 2 8 l 2 θ m 2 ) ∴ V 1 = m g l ( a 2 8 l 2 ) θ m 2 At Position 2 : K i n e t i c e n e r g y : T 2 = 1 2 I ¯ θ m 2

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Author: BEER

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Chapter 19.3, Problem 19.95P

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The frequency of oscillation when the pipe is given a small rotation about the centroidal axis OO' and released.

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Chapter 19.3, Problem 19.94P

Chapter 19.3, Problem 19.96P

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The frequency of oscillation when the pipe is given a small rotation about the centroidal axis O O ' and released.

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