hwk05_soln - Solution for Homework 5.1 ~v G = ~v A + ~ ~ r...

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Unformatted text preview: Solution for Homework 5.1 ~v G = ~v A + ~ ~ r G/A = x i + L 2 k sin i- cos j = x + L 2 cos i + L 2 sin j v 2 G = x + L 2 cos 2 + L 2 sin 2 = x 2 + ( Lcos ) x + L 2 4 2 T = 1 2 (2 m ) v 2 A + 1 2 ( m ) v 2 G + 1 2 I G 2 = 1 2 (2 m ) x 2 + 1 2 ( m ) x 2 + ( Lcos ) x + L 2 4 2 + 1 2 1 12 mL 2 2 = 1 2 (3 m ) q 2 1 + 1 2 ( mcos ) q 1 q 2 + 1 2 1 3 m q 2 2 where q 1 = x and q 2 = L . Therefore, [ M ] = [ m ] ~ =0 = 3 m m 2 cos m 2 cos m 3 ~ =0 = m 6 18 3 3 2 U = 1 2 kx 2- mg L 2 cos = 1 2 kq 2 1- mg L 2 cos q 2 L Therefore, [ K ] = 2 U q i q j ~ =0 = k mg 2 L cos ~ =0 = k mg 2 L = mg 2 L 2 1 where = kL/mg . Eigenvalue problem : ~ q ( t ) = ~ Xe it- 18 + 2 - 3 - 3 - 2 + 1 X 1 X 2 = where = 2 ( L/ 3 g )....
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This document was uploaded on 12/23/2011.

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hwk05_soln - Solution for Homework 5.1 ~v G = ~v A + ~ ~ r...

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