Quiz 1 January 11, 2010 ECE-202, Section 1Find the one-sided Laplace transform of f(t)(tT)2(t2T)(tT)2(t2T) for T > 0. SOLUTION: From the definition of the Laplace Transform, whose lower limit is 0, and the sifting property of the delta function, the answer is F(s)(tT)2(t2T)(tT)2(t2T)estdt0(tT)2(t2T)estdt0T2e2TsECE-202, Section 2Find the one-sided Laplace transform of f(t)cos(2t)(t2T)sin(2t)(2tT) for T > 0. Use the SIFTING property of the delta function and the DEFINITION of the Laplace Transform.
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Limit of a function, Dirac delta function, one-sided Laplace transform, e st dt