- #1
izen
- 51
- 0
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