# pset3 - && 1 1 1 Obtain the transfer function for...

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ME3015 Fall 2011 PROBLEM SET #3 (25 points). Document as outlined in the course admin letter. Due: The beginning of Lesson 9 (September 21). 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 . 2. (6 points) Consider the following system in state-space representation. [ ] = + = x x y u x x b a x x & & & &

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Unformatted text preview: & & 1 1 1 Obtain the transfer function for this system. Problems 3 and 4 on the back side. m k δ y (Origin: Equilibrium position) J Moment of Inertia θ u mg R Neutral length without MASS 3. (6 points) Find the transfer function from E i ( s ) to E O ( s ) for the electrical system shown below: 4. (7 points)Consider the electrical circuit shown below. R C e o ( t ) i e i ( t ) (a) Obtain the transfer function from the input voltage e i ( t ) to output voltage e o ( t ) in the s domain. (b) Plot e o ( t ) versus time when e i ( t ) is given as ≥ < = ) ( t E t t e i where E is a constant voltage. e i ( t ) R 1 C R 2 R 3 e o ( t ) R 4...
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