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Control system miscellaneous

  1. The first two rows of Routh's tabulation of a third order equation are as follows.
    s322
    s344

    This means there are
    1. two roots at s = ± j and one root in right half s-plane
    2. two roots at s = ± j2 and one root in left half s-plane
    3. two roots at s = ± j2 and one root in right half s-plane
    4. two roots at s = ± j and one root in left half s-plane
Correct Option: D

Two roots at s = ±j and one in left halfs-plane

s322
s344

Characteristic equation is A(s) = 2s3 + 4s2 + 2s + 4 = 0
⇒ s3 + 2s2 + s + 2 = 0
⇒ (s + 2) (s2 + 1) = 0
⇒ s = – 2, s = ± j



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