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Unformatted text preview: ASE 330M Linear System Analysis Unique Number: 12495, Spring 2006 Homework #3 Impulse & Step Responses Convolution Integral Date given: February 16, 2006 Date Due: February 28, 2006 1. An LTI system has an impulse response h ( t ) = ( e- t + sin t ) u ( t ). (a) Evaluate the step response g ( t ) for this system. (b) Find the output of this system resulting from an input x ( t ) = u ( t + 2)- u ( t- 2). 2. An LTI system with zero initial energy exhibits an output y ( t ) = (1- e- 2 t cos t ) u ( t- 1) when an input x ( t ) = u ( t- 1) is applied. Evaluate the impulse response h ( t ) for this system. 3. Consider the motion of an automobile on a level surface. The output variable of interest is the speed of the vehicle v ( t ) which is governed by the following dynamics: m ( t ) v ( t ) + k f v ( t ) = x ( t ) where m ( t ) is the instantaneous mass of the vehicle, k f is a friction related positive constant, and x ( t ) is the input force acting on the vehicle. Determine the impulse response. For your) is the input force acting on the vehicle....
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This note was uploaded on 09/25/2011 for the course ASE 18510 taught by Professor Jeannefalcon during the Spring '10 term at University of Texas at Austin.
- Spring '10