GATE EE · Signals And Systems

Laplace Transform Practice Questions

Generate GATE-level questions on Laplace Transform. Focus on: 1. Region of Convergence (ROC) and its properties. 2. Transform pairs and properties: Time-shifting, Differentiation, and Integration. 3. Solving differential equations and System function H(s).

23 questions · 3 PYQs · 0 AI practice · GATE EE 2027

Q21GATE 2004MCQ

Consider the function, $F(s)=\frac{5}{s(s^{2}+3s+2)}$ , where F(s) is the Laplace transform of the of the function f(t). The initial value of f(t) is equal to

🚀 Solve in Practice Mode

📖 Explanation

$F(s)=\frac{1}{s(s^{2+}3s+2)}$ By initial value theorem, $\lim_{t \to 0}f(t)=\lim_{s \to \infty }sF(t)=\lim_{s \to \infty }\frac{5 \times s}{s(s^{2+}3s+2)}=0$

Q22GATE 2002MCQ

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

🚀 Solve in Practice Mode

📖 Explanation

$\text{Final value}=\lim_{s \to 0}sY(s)$

Q23GATE 2001MCQ

Given the relationship between the input u(t) and the output y(t) to be $y(t)=\int_{0}^{t}(2+t-\tau )e^{-3(t-\tau )}u(\tau )d\tau$ , the transfer function Y(s)/U(s) is

🚀 Solve in Practice Mode

📖 Explanation

\begin{aligned} y(t)&=\int_{0}^{t}(2+t-\tau )e^{-3(t-\tau )} u(\tau )d\tau \\ y(t)&=\$[(2+t)e^{-3t}]\$\times u(t) \\ \therefore \; H(s)&=\frac{2}{s+3}+\frac{1}{(s+3)^2} \\ \therefore \; T.F.&=H(s)=\frac{2s+7}{(s+3)^2} \end{aligned}

Want unlimited AI-generated Laplace Transform questions?

Start practising for free →