# Laplace Transform MCQ

1. Consider a linear time-invariant system with transfer function

If the input is cos(t) and the steady-state output is A cos (t+α), then the value of A is

1. 0.90
2. 0.707
3. 0.84
4. 0.50

2. The solution of the differential equation, for t > 0, y”(t) + 2y'(t) + y(t) = 0 with initial conditions y(0) = 0 and y'(0) = 1, is (u(t) denotes the unit step function),

1. te-t u(t)
2. (e-1 – te-t) u(t)
3. (-e-t + te-t) u(t)
4. e-t u(t)

3. The laplace transform of f(t) = e2t sin(5t) u(t) is

4. Which one of the following statements is not true for a continous time causal and stable LTI system?

1. All the poles of the system must lie on the left side of the jω-axis.
2. Zeros of the system can lie anywhere in the s-plane.
3. All the poles must lie within |s| = 1.
4. All the roots of the characteristics equation must be located on the left side of the jω-axis.

5. Consider a causal LTI system characterized by differential equation . The response of the system to the input , where u(t) denotes the unit step function, is

6. The transfer function of a system is . The steady state output y(t) is A cos(2t + Φ) for the input cos(2t). The values of A and Φ, respectively are?

7. The laplace transform of is s-3/2. The laplace transform of is

1. s-1/2
2. s1/2
3. s3/2

8. The unilateral laplace transform of f(t) is . The unilateral laplace transform of t f(t) is

9. Let the laplace transform of a function f(t) which exists for t > 0 be Ft(s) and the laplace transform of its delayed version f(t-τ) be F2(s). F*1(s) be the complex conjugate of F1(s) with the laplace variable set as s = σ + jω. If , then the inverse laplace transform of G(s) is

1. an ideal impulse δ(t)
2. an ideal delayed impulse δ(t-τ)
3. an ideal step function u(t)
4. an ideal delayed step function u(t-τ)

10. The laplace transform of g(t) is

11. The laplace transform of (t2 – 2t) u(t-1) is

1. None of the above