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118_Problem CHAPTER 10 - PROBLEM 10.99 Bar ABC of length 2a...

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PROBLEM 10.99 Bar ABC of length 2 a and negligible weight is hinged at C to a drum of radius a as shown. Knowing that the constant of each spring is k and that the springs are undeformed when 1 2 0, θ θ = = determine the range of values of P for which the equilibrium position 1 2 0 θ θ = = is stable. SOLUTION Have ( ) ( ) ( ) 2 2 2 1 2 1 2 1 1 sin sin 2 cos cos 2 2 θ θ θ θ θ = + + + + V k a k a a P a a Then ( ) 2 1 2 1 1 1 sin sin cos 2 sin θ θ θ θ θ = + V ka Pa 2 1 1 2 1 1 sin 2 cos sin 2 sin 2 θ θ θ θ = + ka Pa and ( ) 2 2 1 1 2 1 2 1 cos2 sin sin 2 cos θ θ θ θ θ = V ka Pa 2 2 1 2 1 2 cos cos θ θ θ θ = V ka Also ( ) 2 2 2 1 2 2 2 2 sin sin cos sin θ θ θ
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