Analytical Mech Homework Solutions 164

Analytical Mech Homework Solutions 164 - 1 Chapter 11 11.1...

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1 Chapter 11 11.1 (a) 2 2 () 2 kk Vx x x =+ 2 2 k Vk x x =− At equilibrium, 0 V ′ = 13 x k = 2 3 2 k x ′′ 23 xk k k = =+ = > 0 Stable (b) ( ) bx k x e = bx bx e b k x e −− At equilibrium 0 bx bx ke bkxe = 1 x b = 2 bx bx bx V bke bkxe b kxe ′′=− + 11 1 1 20 xb Vb k e b k e b k e = + < Unstable (c) 42 2 kx bx 32 Vkx b x At equilibrium kx b x 0 = 0, 2 22 12 2 2 0 2 x b = < 0 Unstable 2 2 62 4 b b k b = 0 > Stable (d) for case (a) 2 3 k m ω = 2 3 3 m Ts k π == = for case (c) at 2 2 2 4 kb m = 2 2 2 4 m kb = 11.2 (, ) 2 4 V x y k x
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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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