Question

find the laplace transform of the function

Answer 1

f(t)=2 0<=t<T
1 t>=T

Answer 2

use the definition of LT
tried it ? where r u stuck ?

Answer 3

I get
2/s -(1/s)*Exp[-sT]

not sure if im right, it is my first time doing this!

Answer 4

\[\int\limits_{0}^{T}2*e ^{st}dt+\int\limits_{T}^{\infty}e ^{st}dt\]

Answer 5

right?

Answer 6

yes.

Answer 7

isn't it e^(-st)
insted of e^(st)

Answer 8

sorry yes i forgot to type them in

Answer 9

so would that be correct if i just integrate them ?

Answer 10

yes just integrate them

Answer 11

so, 2 e^(-st)/(-s) | 0 to T -----> 2 e^(-sT)/(-s) - 2/(-s)
and
e^(-st)/ (-s) | T to infty -----> 0-e^(-sT)/(-s)
got this integration part ?
now we add them...

Answer 12

2 e^(-sT)/(-s) - 2/(-s)-e^(-sT)/(-s) = e^(-sT)/(-s) + 2/s = (2- e^(-sT)) /s
is that understandable ? or should i use latex ?

Answer 13

No worries i use mathematica ! thanks!

Answer 14

ok, welcome ^_^