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Question 3 - 9 marks A particle of mass m is constrained to move on a smooth fixed wire with the shape y = cosh x, where the y-axis is vertically upwards and the only force is that of gravity, which acts in the negative y-direction. (a) How many degrees of freedom does this system have? State appropriate generalised coordinates for this system. [1] (b) Find the speed in terms of the stated generalised coordinates, and determine the Lagrangian. [4] (c) Hence show that the equation of motion of the particle is x cosh2 x + 1/2 sinh 2.c = where g is the magnitude of the acceleration due to gravity. [4]

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