laplace transform of 0051t0051tdel where del is a variable f

laplace transform of -0.05*1(t)+0.05*1(t-del) where del is a variable for a time shift

Solution

I think the correct notation of the expression will be -0.05 u(t) + 0.05 u(t-del) where u(t) stands for unit step function and del is a variable for time shift.

u(t) is defined as

u(t) = 0 , for t<0,

= 1, for t>=0

L(u(t)) = 1/s

we know that if f(t) is a continuous time function or piece wise continuous function then laplace transform of f(t) will be L(f(t))= F(S) and if f(t) is time shifted then L(f(t-a))= e^-as F(s) here a is variable for time shift.

Hence for the given function Laplace transform will be,

-0.05(1/s) + 0.05(1/s) e^{-del s}