Question

The differential equation $100\frac{d^{2}y}{d{t}^2}-20\frac{dy}{dt}+y=x\left(t\right)$ describes a system with an input $x\left(t\right)$ and an output $y\left(t\right)$.The system, which is initially relaxed is excited by a unit step input. The output $y\left(t\right)$ can be represented by the waveform

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$100\frac{d^{2}y}{d{t}^2}-20\frac{dy}{dt}+y=x\left(t\right)$

Taking Laplace transform of both sides
$100s^{2}Y\left(s\right)-20sY\left(s\right)+Y\left(s\right)=\frac{X\left(s\right)}{s}$

$\Rightarrow \frac{Y\left(s\right)}{X\left(s\right)}=\frac{1/s}{(100s^2-20s+1)}=\frac{1}{s(10s-1{)}^2}$

$Polesareats=\frac{1}{10},\frac{1}{10},0$

As poles are on the right-hand side of s-plane so given system is unstable system.
Only option(a) represents unstable system