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The response c(t) of a system to an input r(t) is given by the following differential equation :
d2c(t) + 3 dc(t) + 5c(t) = 5 r(t) dt2 dt
The transfer function of the system is given by
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G(s) = 5 s2 + 3s + 5 -
G(s) = 5 s2 + 3s + s -
G(s) = 3s s2 + 3s + 5 -
G(s) = s + 3 s2 + 3s + 5
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Correct Option: A
Given equation is,
| + 3 | + 5 c(t) = 5 r(t) | |||
| dt2 | dt |
Taking Laplace transform, we get
(s2 + 3s + 5) C (s) = 5 R (s)
| ∴ | = | |||
| R(s) | s2 + 3s + 5 |
