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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?
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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) ]
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