118_Problem CHAPTER 10

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

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Unformatted text preview: PROBLEM 10.99 Bar ABC of length 2a 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, determine the range of values of P for which the equilibrium position 1 = 2 = 0 is stable. SOLUTION Have V = 1 1 2 2 k ( a 2 ) + k ( a sin 1 + a sin 2 ) + P ( 2a cos1 + a cos 2 ) 2 2 V = ka 2 ( sin 1 + sin 2 ) cos1 - 2Pa sin 1 1 1 = ka 2 sin 21 + cos1 sin 2 - 2Pa sin 1 2 and 2V = ka 2 ( cos 21 - sin 1 sin 2 ) - 2Pa cos1 12 2V = ka 2 cos1 cos 2 1 2 Then Also V = ka 2 2 + ka 2 ( sin 1 + sin 2 ) cos 2 - Pa sin 2 2 1 = ka 2 2 + ka 2 sin 1 cos 2 + sin 2 2 - Pa sin 2 2 and When 2V = ka 2 + ka 2 ( - sin 1 sin 2 + cos 2 2 ) - Pa cos 2 2 2 1 = 2 = 0 V =0 1 2V = ka 2 1 2 V =0 2 2V = ka 2 - 2 Pa 12 2V = ka 2 + ka 2 - Pa = 2ka 2 - Pa 2 2 ...
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