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Using standard transformations between Cartesian and Cylindrical coordinate systems
x=rcos(theta) y=rsin(theta)
r=sqrt(x^2+y^2)
z=z
Theta= arctan(y/x)
Develop equations for the cylindrical velocity components Vr and Vtheta as a function of the Cartesian velocity components, u and v.
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What forms do the equations of motion for an idealized string take if either (a) the linear density varies with position, or (b) the string hangs vertically supported only at the upper end?
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