39. The unit staircase function is defined as follows: f(t) = n if n-1§1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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39. The unit staircase function is defined as follows:
f() = n if n-l{i<n, n= 1,2,3....
(a) Sketch the graph of ƒ to see why its name is appropri-
ate. (b) Show that
f() = E
u(t – n)
n=0
for all 1 2 0. (c) Assume that the Laplace transform of the
infinite series in part (b) can be taken termwise (it can).
Apply the geometric series to obtain the result
1
Lif(()} =
s(1 – e-5)
Transcribed Image Text:39. The unit staircase function is defined as follows: f() = n if n-l{i<n, n= 1,2,3.... (a) Sketch the graph of ƒ to see why its name is appropri- ate. (b) Show that f() = E u(t – n) n=0 for all 1 2 0. (c) Assume that the Laplace transform of the infinite series in part (b) can be taken termwise (it can). Apply the geometric series to obtain the result 1 Lif(()} = s(1 – e-5)
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