The laplace transform for ramp function with a time delay can be expressed as follows

Jerold 2020-10-26 Answered
The laplace transform for ramp function with a time delay can be expressed as follows
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Expert Answer

Khribechy
Answered 2020-10-27 Author has 100 answers

Step 1
Let the time delay is T,
So the ramp function will be
f(t)=(tT)u(tT)
Where
u(tT)={1t>T0t
Step 2
Let the Laplace transform of f(t) is F(s)
So the Laplace transform is
F(s)=0f(t)estdt
F(s)=TT(tT)estdt
let
x=t-T
dx=dt
So we have
F(s)=0xes(x+T)dx
F(s)=esT0xesxdx
F(s)=esTs2

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