Final Exam Practice

Final Exam Practice - Problem 1 a Given that F s = Lcfw f(t...

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Problem 1 a) Given that , use the defining integral for the Laplace transform show that () ()} Fs ft = L{ {} dF s tf t ds =− L . b) Find the { } sinh ( ) ktu t L . Hint: ( ) 1 2 sinh kt kt kt e e . c) Find 2 1 2 51 23 L 21 ss s ++ d) Find 1 2 6 42 0 s + L
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Problem 2 For the circuit shown in the figure below: a) Use Kirchhoff’s laws to obtain a differential equation for the response ( ) c vt . Hint: Apply Kirchhoff’s voltage law to the left-hand loop and Kirchhoff’s current law at node ‘a’ b) Substitute the element values and find the roots of the characteristic equation. c) What is the form of the source-free response? d) Find ( ) c for all 0 t + if (0 ) 1 and (0 ) 0 c vi −− = = .
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Problem 3 The current source in the circuit shown in part (a) of the following figure generates the waveform shown in part (b) of that figure. a) What is the impulse response ( ) ht of this circuit? b) Find the voltage () o vt by evaluating the convolution integral (not by finding the inverse Laplace transform of the product of Laplace transforms).
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This note was uploaded on 02/18/2010 for the course ECET 232 taught by Professor Gla during the Spring '07 term at NJIT.

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Final Exam Practice - Problem 1 a Given that F s = Lcfw f(t...

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