HW7 - ME 375 HOMEWORK # 7 Spring 2009 Out: March 4, 2009...

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ME 375 HOMEWORK # 7 Spring 2009 Out: March 4, 2009 Due: March 11, 2009 (at the beginning of class) PROBLEM 1: (30%) Consider the following differential equation of motion relating an input f(t) to the corresponding output x(t) : () 2 () 2 () () (0 ) 0 ) x tx t f t x x ++= = = ±± ± ± Answer the following questions: (a) Calculate the transfer function relating the input Laplace transform F(s) to the output Laplace transform X(s) . (b) For a unit step input, solve for the steady-state output using the final value theorem. (c) Calculate the frequency response function between the input and output. (d) For f ( t ) = 1 for t > 0, find the steady-state output using the frequency response function. (e) For f ( t ) = sin 0.1 t + cos 1.5 t , find the steady-state output using the frequency response function. (f) For x ( t ) = sin t 0.1 + 2 in the steady state, find the forcing function. (g) Now suppose that you use an imperfect sensor to measure x(t) such that 0.1 ( ) ( ) ( ) yt xt + = ± where y(t) is the measurement of x(t) . Calculate the frequency response function between the true output, x(t) , and the sensor output,
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HW7 - ME 375 HOMEWORK # 7 Spring 2009 Out: March 4, 2009...

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