812_Dynamics 11ed Manual

812_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 22 where δ= (b tan (θ ) + y) 2 + b2 − (b tan (θ ) )2 + b2 = sin ( θ ) y for small y thus 1 22 2 M y' + k sin ( θ ) y = 0 2 M y'' + 2k sin ( θ ) y = 0 2 ⎛ 2k sin ( θ ) 2 ⎞ ⎟y = 0 y'' + ⎜ ⎝M⎠ 2k sin ( θ ) M ωn = 2 2π τ= τ = 2.81 s ωn *Problem 22-36 Determine the natural period of vibration of the sphere of mass M. Neglect the mass of the rod and the size of the sphere. Given: M = 3 kg k = 500 a = 300 mm b = 300 mm N m Solution: T+V= 2 1 21 2 M ( bθ' ) + k ( aθ ) 2 2 2 2 M b θ'' + k a θ = 0 θ'' + ka Mb 2 θ=0 2 τ = 2π Mb ka 2 τ = 0.487 s 810 ...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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