I have a exercise and i can't do a part of it. I've a transfert function G(s) = 1/(s+1) and u(t), the entering signal:
u(t) is
1+2t for 0<=t<1
t-1 for t>=1
I have to find y(t), the outcoming signal of the system.
I find, correctly, the signal y(t) about the first part of u(t), 1+2t:
y1(t)=2t + e^{-t} -1
First i use laplace transform on u(t), for have U(s) , only the first part
Second i know that Y(s)= G(s)U(s) so, i calculate Y(s) because i've G(s) and U(s)
Antitransform Y(s) for have y(t)
But now i don't know how to find y(t) for the second part, t-1. Could someone tell me how to find it, i'd like to comprend because it's not an homework but an exercise that i do for preparing me to an exam. Thanks!
u(t) is
1+2t for 0<=t<1
t-1 for t>=1
I have to find y(t), the outcoming signal of the system.
I find, correctly, the signal y(t) about the first part of u(t), 1+2t:
y1(t)=2t + e^{-t} -1
First i use laplace transform on u(t), for have U(s) , only the first part
Second i know that Y(s)= G(s)U(s) so, i calculate Y(s) because i've G(s) and U(s)
Antitransform Y(s) for have y(t)
But now i don't know how to find y(t) for the second part, t-1. Could someone tell me how to find it, i'd like to comprend because it's not an homework but an exercise that i do for preparing me to an exam. Thanks!