I need help with transfer functions

Question

I need help to solving these:

I need to rewrite each of these transfer functions:

a) F₁(s) = 1 / (3s + 5)

b) F₂(s) = 5.5 / (3.4s + 1.2)

c) F₃(s) = a / (bs + c)

into the 2 standard forms:

H₁(s)= K1 / (Ts + 1)

H₂(s) = K2 /(s + p)

Answer 1

a) For 1st form divide both numerator and denominator by 5 and you get

H₁₁(s) = 0.2 / (0.6s + 1)

For the second form divide both numerator and denominator by 3 and you get

H₁₂(s) = 1 / (3*(s + 5/3)) = 0.333 / (s + 1.666)

b) For 1st form divide both numerator and denominator by 1.2 and you get

H₁₁(s) = 4.6833 / (2.833s + 1)

For the second form divide both numerator and denominator by 3.4 and you get

H₁₂(s) = 1.618 / (s + 0.353)

c) For 1st form divide both numerator and denominator by c and you get

H₁₁(s) = (a/c) / ((b/c)*s + 1)

For the second form divide both numerator and denominator by b and you get

H₁₂(s) = (a/b) / (s + (c/b))