# HW5soln - ME 375 Homework 5 : Solution February 18, 2009...

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ME 375 Homework 5 : Solution February 18, 2009 Problem 1 v (3) ( t ) + 4¨ v ( t ) + 3˙ v ( t ) = f ( t ) Part A Determine the transfer function V(s) to F(s) Solution: [ s 3 V ( s ) - s 2 v (0) - s ˙ v (0) - ¨ v (0)]+4[ s 2 V ( s ) - sv (0) - ˙ v (0)]+3[ sV ( s ) - v (0)] = F ( s ) [ s 3 + 4 s 2 + 3 s ] V ( s ) - [( s 2 + 4 s + 3) v (0) + ( s + 4)˙ v (0) + ¨ v (0)] = F ( s ) The initial conditions are considered to be zero. The transfer function is : V ( s ) F ( s ) = 1 s 3 + 4 s 2 + 3 s Part B We need to determine the free response: Given: f ( t ) = 0 v (0) = 1 ˙ v (0) = - 1 ¨ v (0) = 2 V ( s ) = ( s 2 + 4 s + 3) v (0) + ( s + 4)˙ v (0) + ¨ v (0) s 3 + 4 s 2 + 3 s 1

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V ( s ) = ( s 2 + 4 s + 3)(1) + ( s + 4)( - 1) + 2 s 3 + 4 s 2 + 3 s Solution : V ( s ) = s 2 + 3 s + 1 s 3 + 4 s 2 + 3 s Part C What are the similarities between Part A and Part B? They both have the same denominator. Part D
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## This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue University.

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HW5soln - ME 375 Homework 5 : Solution February 18, 2009...

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