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Analytical Mech Homework Solutions 24

Analytical Mech Homework Solutions 24 - Fr = mg mk mkd k...

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cos r m mk mkd k F mg x mg t M m M m M = + = + + + m + For the block to just begin to leave the bottom of the box at the top of the vertical oscillations, 0 r F = at m x d = − : 0 mkd mg M m = + ( ) g M m d k + = 3.9 ( ) cos t d x e A t γ ω φ = ( ) ( ) sin cos t t d d d dx e A t e A t dt γ γ ω ω φ γ ω φ = − maxima at ( ) ( ) 0 sin cos d d d t t dt dx ω ω φ γ ω φ + = = ( ) tan d d t γ ω φ ω = − thus the condition of relative maximum occurs every time that t increases by 2 d π ω : 1 2 i i d t t π ω + = + For the i th maximum: ( ) cos i t i d x e A t γ i ω φ = ( ) 1 2 1 1 cos i d t i d i i x e A t e π γ γ ω ω φ + + + = x = 2 1 d d T i i x e
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