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System described by the equation
(i) y′′(t) + 3y′(t) + 2y(t) = x(t)
(ii) y′′(t) + 3y′′(t) = x(t)
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- (i) is stable, (ii) is unstable
- (i) is unstable, (ii) is stable
- Both (i) and (ii) are stable
- Both (i) and (ii) are unstable
Correct Option: A
Given equation
(i) y′′(t) + 3y′(t) + 2y(t) = x(t)
or (s2 + 3s + 1) Y(s) = X(s)
| = | ||
| X(s) | s2 + 3s + 1 |
Roots of characteristic equation
s2 + 3s + 1 = 0
(s + 1) (s + 2) = 0
s = – 1, – 2
Here, all the roots are lie on the left hand side of s-plane hence the system is stable.
(ii) y′′′(t) + 3y′′(t) = x(t)
(s3 + 3s2) Y(s) = X(s)
| = | = | |||
| X(s) | s3 + 3s2 | s2 + (s + 3) |
Since, the two poles are lie on the origin therefore, the given system is unstable.
Hence, alternative (A) is the correct choice.
