A control system is defined by the following mathematical relationshipd2xdt2-6dxdt-5x-121-e2tThe response of the system as t - is

Taking (LT) on both sides nbsp; (s^2+6s+5) X(s)=12 (1s 1s+2 nbsp; ) = 24s(s+2) X(s)=24s(s+2)(s+1)(s+5) Response at t →∞ nbsp; Using final value the ...

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Standard XII

Physics

Newton's Second Law

A control sys...

Question

A control system is defined by the following mathematical relationship

$\frac{d^{2} x}{d t^{2}} + 6 \frac{d x}{d t} + 5 x = 12 (1 - e^{2 t})$

The response of the system as $t \to \infty$ is

x = 6

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x = 2

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x = 2.4

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x = -2

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Solution

The correct option is C x = 2.4
Taking (LT) on both sides

$(s^{2} + 6 s + 5) X (s) = 12 (\frac{1}{s} - \frac{1}{s + 2})$

$= \frac{24}{s (s + 2)}$

$X (s) = \frac{24}{s (s + 2) (s + 1) (s + 5)}$

Response at $t \to \infty$

Using final value theorem

$L t_{t \to \infty} x (t) = L t_{s \to 0} s . X (s)$

$= L t_{s \to 0} \frac{s \times 24}{s (s + 1) (s + 2) (s + 5)} = 2.4$

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A control system is defined by the following mathematical relationship d2xdt2+6dxdt+5x=12(1−e2t) The response of the system as t→∞ is

The correct option is C x = 2.4Taking (LT) on both sides (s2+6s+5) X(s)=12(1s−1s+2) =24s(s+2) X(s)=24s(s+2)(s+1)(s+5) Response at t→∞ Using final value theorem Ltt→∞ x(t)=Lts→0 s.X(s) =Lts→0s×24s(s+1)(s+2)(s+5)=2.4

A control system is defined by the following mathematical relationship

$\frac{d^{2} x}{d t^{2}} + 6 \frac{d x}{d t} + 5 x = 12 (1 - e^{2 t})$

The response of the system as $t \to \infty$ is