problem15_68

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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15.68: (a) The displacement of the string at any point is . sin ) sin ( ) , ( SW t kx A t x y ϖ = For the fundamental mode , 2 L = λ so at the midpoint of the string , 1 ) 2 )( 2 sin( sin = λ = L π kx and . sin SW t A y ϖ = Taking derivatives gives , cos SW ωt ωA v t y y = = with maximum value , sin and , SW 2 SW max ωt A ω a ωA v t v y y y - = = = with maximum value . SW 2 max A ω a y = Dividing these gives s, rad
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• Fundamental frequency, Mode shape, ASW sin ωt

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