assign05 - 2 ) ( a s s + ? Keep in mind the significance of...

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SYSC 3600 – Assignment #5 1/. How will the system below respond assuming that V IN is a half cycle of a sine wave (as drawn)? Derive an expression for V OUT . Your expression will (or at least should) involves the constants R and C . 2/. Consider the system shown below. A mass is mounted on a base using a spring and a damper. The system input is the position of the base, and the system output is the position of the mass. 2/. What is the defining differential equation for the system? What does this equation look like when transformed to the frequency domain? Be sure to include the initial conditions. What is the transfer function for the system? What are the units for the transfer function? 3/. The table of Laplace transform pairs in the notes tells us that the inverse transform of 2 ) ( 1 a s + is at te . What is the inverse transform of
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Unformatted text preview: 2 ) ( a s s + ? Keep in mind the significance of multiplying by s in the frequency domain. 4/. Assuming that m = 10 kg, k = 1000 N/m, and c = 200 N-s/m, what is the impulse response of the system of question 2? What are the units for the impulse response? Your answer to question 3 should come in handy. Does your answer make sense for large values of t ? 5/. Assuming the values of question 4 (i.e. the values for which you have calculated the system's impulse response) use convolution to determine how the system will respond if the base is suddenly raised by 2cm. Does your answer make sense for large values of t ? References (you may find these useful in completing this assignment): ( ) 2 2 ) cos( ) sin( ) sin( p a px p px a e dx px e ax ax + − = ∫ ) 1 ( 2 − = ∫ ax a e dx xe ax ax...
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This note was uploaded on 07/16/2009 for the course SYSC 3600 taught by Professor John bryant during the Winter '08 term at Carleton CA.

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assign05 - 2 ) ( a s s + ? Keep in mind the significance of...

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