-
The error response of a second order system to a step input is obtained as
E (t) = 1.66 e–8t sin (6t + 37°).
The damping ratio is—
-
- 0.4
- 0.5
- 0.8
- 1.0
- 0.4
Correct Option: C
Given E(t) = 1.66 e–8t sin (6t + 37°) …(A)
on comparing above equation (A) with the standard equation
| E(t) = | e–ωnt sin (ωn√1 – ξ2 t ± φ) | |
| √1 - ξ2 |
we get,
ωn √1 – ξ2 = 6 …(i)
ξωn = 8 …(ii)
From (i) and (ii)
√1 – ξ2 /ξ
| = | = | ||
| 8 | 4 |
| or, | = | ⇒ 16 - 16ξ2 = 9ξ2 | ||
| ξ2 | 16 |
25ξ2 = 16
| ξ = | = 0.8 | |
| 5 |
