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Which of the following is the transfer function of: dc(t)dt+2c(t)=r(t)\frac{d c(t)}{d t} + 2 c(t) = r(t)dtdc(t)+2c(t)=r(t)

Question

Which of the following is the transfer function of: $\frac{d c(t)}{d t} + 2 c(t) = r(t)$

$G(s) = \frac{s}{s - 2}$

Solution

Given that,

$\frac{d c(t)}{d t} + 2 c(t) = r(t) \quad \dots(1)$

Transfer function = ?
From equation (1) taking laplace transform
s C(s)+2C(s) = R(s)
(s+2)C(s) = R(s)

$\boxed{\text{T.F.} = \frac{C(s)}{R(s)} = \frac{1}{s + 2}}$

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