A particle of mass (m) slides inside a smooth paraboloid of revolution whose surface is defined by
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A particle of mass \(m\) slides inside a smooth paraboloid of revolution whose surface is defined by \(z=\alpha ho^{2}\), where \(z\) and \(ho\) are cylindrical coordinates.
(a) Write the Lagrangian for the three-dimensional system using the method of Lagrange multipliers.
(b) Find the equations of motion.
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