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Question

# The differential equation 100d2ydt2−20dydt+y=x(t) describes a system with an input x(t) and an output y(t).The system, which is initially relaxed is excited by a unit step input. The output y(t) can be represented by the waveform

A
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B
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C
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D
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Solution

## The correct option is A 100d2ydt2−20dydt+y=x(t) Taking Laplace transform of both sides 100s2Y(s)−20sY(s)+Y(s)=X(s)s ⇒Y(s)X(s)=1/s(100s2−20s+1)=1s(10s−1)2 Poles are at s=110,110,0 As poles are on the right-hand side of s-plane so given system is unstable system. Only option(a) represents unstable system

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