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The first two rows of Routh's tabulation of a third order equation are as follows.
s3 2 2 s3 4 4
This means there are
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- two roots at s = ± j and one root in right half s-plane
- two roots at s = ± j2 and one root in left half s-plane
- two roots at s = ± j2 and one root in right half s-plane
- two roots at s = ± j and one root in left half s-plane
- two roots at s = ± j and one root in right half s-plane
Correct Option: D
Two roots at s = ±j and one in left halfs-plane
s3 | 2 | 2 |
s3 | 4 | 4 |
Characteristic equation is A(s) = 2s3 + 4s2 + 2s + 4 = 0
⇒ s3 + 2s2 + s + 2 = 0
⇒ (s + 2) (s2 + 1) = 0
⇒ s = – 2, s = ± j