Analytical Mech Homework Solutions 168

Analytical Mech Homework Solutions 168 - 5 b 3 V = mg ( h1...

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5 ()( ) 12 3 cos cos 8 b Vm gh h m gab a a θ θθ   =+ = + − +     () 3 sin sin 8 aab ab g ab aa + + =− + + Equilibrium occurs at 0 o = 2 3 cos cos 8 ga b + +    ′′ + +     ( 2 0 3 35 88 m g abba + + + ) 5 a 0 03 Vf o r b >> Therefore, the equilibrium is stable for 3 5 b a < 11.8 From Problem 11.4, we have ( ) 1 2 2 22 2 2 2 2 () 2 2 2 2 1 y V y k y l l y mgy k y l mgy l =−+ =−+− Expanding the square root for small y l 1 2 11 1 1 ... 28 yy y ll l 4 4 + + 4 222 2 2 4 y Vy ky l y m g y l ≈− + 3 2 2 k l m g at equilibrium, 1 2 3 0 2 mgl k =⇒= 2 2 6 k l ′′= 1 2 3 2 2 1 2 3 3 3 2 2 6 6 ym g l k km g l m g Vk lk l = == 1 33 3 66 g g mm l l m ω = 1 6 k
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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