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The motion of a particle is given by x = A sin^3(\omegat). What is the amplitude of the particle's motion? (b) What is the expression for the particle's velocity, v? (c) What is the expression for the particle's acceleration, a?

Added Thu, 30 Jul '15

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sin^3(wt) =[3sin(wt)-sin(3wt)]/4

Asin^3(wt) =A[3sin(wt)-sin(3wt)]/4

x=(A/4)[3sin(wt)-sin(3wt)]

amplitude = (A/4)

b)v =d(x)/dt =d((A/4)[3sin(wt)-sin(3wt)])/dt =A/4[3wcos(wt)-3wcos(3wt)] =(3wA)/4 [cos(wt)-cos(3wt)]

c) accelaration =a =d^2(x)/dx^2 =d/dx((3wA)/4 [cos(wt)-cos(3wt)])

=(3wA)/4 [-wsin(wt)+3wsin(3wt) ]=(3w^2A)/4 [-sin(wt)+3sin(3wt) ]

Added Thu, 30 Jul '15

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