engineering recuitment GATE IN Test Series 2023-24 Mock Test Signals and Systems Laplace Transform Transfer Function From Differential Equation
Consider a system H(s) described by a differential equation:
\(\frac{{dy\left( t \right)}}{{dt}} + 2y\left( t \right) = \frac{{{d^2}x\left( t \right)}}{{d{t^2}}} + 2\frac{{dx\left( t \right)}}{{dt}} - 3x\left( t \right)\)
From the above transfer function, we conclude that:1
Inverse system is both casual and stable
2
Steady-state value of the inverse system is 4
3
System has only one pole and two zero’s
4
If \(X\left( s \right) = \frac{1}{{\left( {s - 1} \right)\left( {s + 3} \right)}}\) then y(t) = e-2tu(t)