this is done by the Lagrangian method.take a variation of kinetic energy expressions and same with potential energy and then combine it with virtual work to get the equation of motion.Variation calculus is needed.If you can get a differential equation representing motion by another method then it's cool. z12,=0.5x,?X2Z2A roller coaster is being designed on a parabolic track that rotates at a constant speed as seen in the figure above.Assume the cart rolls on the track as a frictionless point-mass of 100-kg. Determine the equations of motion interms of the distance from the lowest point, q1 = 12.a. What is the kinetic energy of the cart?b. What is the potential energy of the cart?c. What is the equation of motion for the cart?

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Answered: z12,=0.5x,? X2 Z2 A roller coaster is…

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