- #1

izen

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## Homework Statement

f(t) = cos (pi*t) if 1[itex]\leq[/itex] t <4 and 0 elsewhere

using unit step functions to find Laplace Transform

## Homework Equations

## The Attempt at a Solution

I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4)

in order to use the second shifting theorem f(t) must in the format of f(t-a) in this case a = 1 and 4.

I add 1 and subtract 1 , add 4 and subtract 4 and I get

f(t) = cos(pi(t-1+1) u(t-1) - cos(pi(t-4+4) u(t-4)

= cos (pi(t-1)) u(t-1) +u(t-1) - cos(pi*(t-4) u(t-4)+u(t-4) << i think this step is not correct

It should get -cos (pi(t-1)) u(t-1) - cos(pi*(t-4) u(t-4) but i don't know how to get there

please help thank you