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Actual: Recall `u(t)` is the unit-step function. 1. ℒ`{u(t)}=1/s` 2. ℒ`{u(t-a)}=e^(-as)/s` 3. Time Displacement Theorem: If `F(s)=` ℒ`{f(t)}` then ℒ`{u(t-a)g(t-a)}=e^(-as)G(s)` [You can see what the left hand side of this expression means in the section Products Involving Unit Step Functions.]
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Definition: The unit step function, `u(t)`, is defined as `u(t)={: {(0, t 0), (1, t 0) :}` That is, u is a function of time t, and u has value zero when time is negative (before we flip the switch); and value one when time is positive (from when we flip the switch).

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Note that f(t)-f(t-2) is just a single period of f(t) in the range [0,2], i.e. f(t)-f(t-2)=u(t)-u(t-1) tag{1} the Laplace transform of Convolution using Integration.

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