Analytical Mech Homework Solutions 22

# Analytical Mech Homework Solutions 22 - CHAPTER 3...

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CHAPTER 3 OSCILLATIONS 3.1 ( ) [ ] 1 0.002sin 2 512 x s t m π = ( )( )( ) max 0.002 2 512 6.43 m m x s s π = = ± ( )( ) ( ) 2 2 4 max 2 2 0.002 2 512 2.07 10 m m x s s π = = × ±± 3.2 0.1sin x t ω = D [ m ] 0.1 cos m x t s ω ω = D D ± When t = 0, x = 0 and 0.5 0.1 m x s ω = = D ± 1 5 s ω = D 2 1.26 T s π ω = = D 3.3 ( ) cos sin x x t x t t ω ω ω = + D D D D ± D and 2 f ω π = D ( ) ( ) [ ] 0.25cos 20 0.00159sin 20 x t t π π = + m 3.4 ( ) cos cos cos sin sin α β α β α = + β ( ) cos cos cos sin sin x A t A t A t ω φ φ ω φ = = + D D ω D cos sin x t t ω ω = Α + Β D D , cos A φ Α = , sin A φ Β = 3.5 2 2 2 2 1 1 2 1 1 1 1 2 2 2 2 mx kx mx kx + = + ± ± 2 ( ) ( ) 2 2 2 2 1 2 2 1 k x x
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