ME410_SampleExam1

ME410_SampleExam1 - o in terms of the input voltage V 1 ,...

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ME410/610 Spring 2010 Sample Exam 1 October 5 Closed notes and book. No calculators or electronic devices allowed. Please show all your work for full credit. Problem: What is the mathematical definition of the Laplace Transform? Problem: Why is the Laplace Transform important? Problem : For the closed-loop transfer function below, is the system stable? Why? 2 3 ) 6 )( 2 ( ) ( 2 + + + = s s s s s H Problem : Find f(t) given the Laplace Transform: 4 2 3 ) ( 2 + + = s s s F Problem : Use Mason’s Rule to find the transfer function between R(s) and Y(s) for the following block diagram.
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Problem : Consider the system shown below: ) 2 )( 1 ( 1 ) ( + + = s s s G ; 1 ) ( = s F (a) What is the order of the closed-loop feedback system? (b) What gain would give the system step response a rise time of less than or equal to 0.18 seconds? Problem : Find the transfer function that relates the input V 1 (s) to the output V 2 (s). Problem: Derive the output voltage V
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Unformatted text preview: o in terms of the input voltage V 1 , and components. Problem: Derive the output voltage V in terms of the input voltages and the resistors. Problem: (a) Determine the equation(s) of motion for the spring-mass-damper cart system shown below. Show all your work and clearly justify your steps. (b) Find the transfer function between the applied force and the motion of mass M 1 . Problem: Estimate the transfer function for an unknown system with the following step response: Problem: Find the inverse Laplace transform for the following: ( ) ) ( ) ( b s k a s k s F + + = where k , a , b are constants The following relationships may be useful: at at at at e a s s a bt e b a s a s bt b s s e bt e b a s b bt b s b = + = + + + = + = + = + + = + 1 ) ( ) cos( ) ( ) cos( a s 1 ) sin( ) ( ) sin( 2 2 2 2 2 2 2 2...
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ME410_SampleExam1 - o in terms of the input voltage V 1 ,...

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