Unformatted text preview: i) That the angular momentum of the mass is conserved. ii) That the motion of the object is restricted to the z =0 plane. 3) [15 points] A simple pendulum of length b and bob mass m is attached to a massless support moving vertically upwards with constant acceleration α . Determine (a) the equations of motion and (b) the period for small oscillations. 4) [15 points] A particle is free to slide along a smooth cycloidal trough whose surface is given by the parametric equations: x = a 4 2 " sin2 ( ) y = " a 4 1 " cos2 ( ) where ! " ! # and a is a constant. a) Find the Lagrangian function and the equation of motion of the particle. b) Show that the particle undergoes simple harmonic motion without any small angle approximation. Total 60 points...
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 Fall '08
 Staff
 Differential Equations, mechanics, Mass, Simple Harmonic Motion, Work, #, smooth cycloidal trough

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