Consider the two functions f(t) = h(t)h(3 t) and g(t) = h(t) h(t 3): (a) Are the two functions identical? (b) Show that L[f(t)] = L[g(t): Solution. (a) We have f(t) = 1; 0 t 3 0; t > 3 and g(t) = 1; 0 t < 3 0; t 3 So the two functions are equal for all t 6= 3 and so they are not identical. (b) We have L[f(t)] = L[g(t)] = Z 3 0 estdt = 1 e3s s ; s > 0: Thus, both functions f(t) and g(t) have the same Laplace transform even though they are not identical. However, they are equal on the interval(s) where they are both continuous The inverse Laplace transform possesses a linear property as indicated in the following result.
Posted on: Sun, 20 Oct 2013 01:44:28 +0000
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