Transfer function: 5 / s2 +2s +1
These are the steps Ive done:
Kωn2 / s(s2 + 2ςωns + ωn2 )
Y(s) = 1 / s + A1 / s-P1 + A2 / s-P2
y(s) = 1 + A1expP1t + A2expP2t
P1 + P2 = poles are equal to the roots
S2 +2ςωns + ωn2 = 0
P1, P2 = -2ςωn +- √ 4ς2ωn2 - 4ωn2 / 2 = ςωn +- ωn √ ς2 1
A1 = -(kς / 2√ ς2 1) k / 2
A2 = (kς / 2√ ς2 1) k / 2
But I dont know how to find the poles and damping ratio please help!
These are the steps Ive done:
Kωn2 / s(s2 + 2ςωns + ωn2 )
Y(s) = 1 / s + A1 / s-P1 + A2 / s-P2
y(s) = 1 + A1expP1t + A2expP2t
P1 + P2 = poles are equal to the roots
S2 +2ςωns + ωn2 = 0
P1, P2 = -2ςωn +- √ 4ς2ωn2 - 4ωn2 / 2 = ςωn +- ωn √ ς2 1
A1 = -(kς / 2√ ς2 1) k / 2
A2 = (kς / 2√ ς2 1) k / 2
But I dont know how to find the poles and damping ratio please help!