795_Dynamics 11ed Manual

795_Dynamics 11ed Manual - = k 500 N m = Solution: M gl sin...

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Engineering Mechanics - Dynamics Chapter 22 *Problem 22-12 If the lower end of the slender rod of mass M is displaced a small amount and released from rest, determine the natural frequency of vibration. Each spring has a stiffness k and is unstretched when the rod is hanging vertically. Given: M 30 kg = l 1m
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Unformatted text preview: = k 500 N m = Solution: M gl sin ( ) 2 kl sin ( ) l cos ( ) + M 2 l ( ) 2 3 '' = For small angles 4 M l 2 3 '' M gl 2 kl 2 + ( ) + = '' 3 g 4 l 3 k 2 M + + = n 3 g 4 l 3 k 2 M + = n 5.69 rad s = f n 2 = f 0.91 1 s = 793...
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