hw4 - ASE 330M Linear System Analysis Unique Number: 12880,...

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ASE 330M Linear System Analysis Unique Number: 12880, Spring 2007 Homework #4 Impulse and Step Response for LTI Systems Date given: March 1, 2007 Date Due: March 20, 2007 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 ) = 2 u ( t +3) - 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 calculations, you may assume mass depletion from fuel consumption
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hw4 - ASE 330M Linear System Analysis Unique Number: 12880,...

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