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pset3_sol

# pset3_sol - ME3015 PROBLEM SET#3(25 points Solutions 1(6...

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ME3015 PROBLEM SET #3 (25 points). Solutions 1. (6 points) Assume that the system is initially in equilibrium. The gravitational force of mass causes a static deflection of the spring. The external force u applies as input and the displacement y is the output of the system. Find the state-space representation of the spring-mass-pulley shown below. Then convert the state-space representation to the corresponding transfer function from u to y . Solution Define the tension acting in the wire as T ’= T + k δ where k = mg. Since the displacement y is defined from the equilibrium position, the effect of gravity is not included in the dynamic equations. The equations of motion for the mass and the pulley are given as 2 R k TR J u T y m θ = + = Since R y = , the equation of motion for the pulley can be written as y kR TR y J 2 2 = J = TR 2 R k m k δ y (Origin: Equilibrium position) J Moment of Inertia θ u mg R Neutral length without MASS m y T = m u

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pset3_sol - ME3015 PROBLEM SET#3(25 points Solutions 1(6...

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