series RL analysis using Laplace
Could anyone offer some assistance please?(Thinking)
I have a question which states the following:
L[v(t)] = V(s) = 1/(1+s^s)(1-e^(pi*s)
if an inductor (1 H) and a resistor (1 Ohm) are connected in series then show that the resulting current is,
where f(t) =(sin(t)-cos(t)+e^(-t))u(t)
i am able to analysis the circuit to give the following:
L[di/dt] +L[Ri]=L[v(t)] giving I(s)=1/(s+1)(s^2+1)(1-e^(pi*s))
using partial fractions it becomes:
I am really not sure where to go next, I am sure that 1/(1-e^(-s*pi)) is some kind of geometric series but other than that I am stumped!
I would really appreciate it if someone could point me in the right direction.