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Question

# A control system is represented by the given below differential equation, d2ydt2+5dydt+4y=x(t) has all initial conditions as zero. If an input x(t) = 8 u(t), then output y(t) is,

A

[114e4t+12et]u(t)

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B

[1+14e4t+13et]u(t)

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C

[1+18e4t13et]u(t)

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D
2[1+13e4t43et]u(t)
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Solution

## The correct option is D 2[1+13e−4t−43e−t]u(t) d2ydt2+5dydt+4y=x(t) s2Y(s)+5sY(s)+4Y(s)=X(s) x(t)=8u(t)orX(s)=8s (s2+5s+4)Y(s)=8s Y(s)=8s(s2+5s+4)=As+Bs+4+Cs+1 Y(s)=2s+23(s+4)−83(s+1) y(s)=2[1+13e−4t−43e−t]u(t)

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