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
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),
- te-t u(t)
- (e-1 – te-t) u(t)
- (-e-t + te-t) u(t)
- 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?
- All the poles of the system must lie on the left side of the jω-axis.
- Zeros of the system can lie anywhere in the s-plane.
- All the poles must lie within |s| = 1.
- 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
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
- an ideal impulse δ(t)
- an ideal delayed impulse δ(t-τ)
- an ideal step function u(t)
- 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
- None of the above