Assignment:
Question 1. Find the Laplace transform of 6 cos t + 2e −3t .
Question 2. Find the Laplace transform of 2 cosh t + 2t 3.
Question 3. Find the Laplace transform of 2te −3t.
Question 4. Find the inverse Laplace transform of s/s+2.
Question 5. Find the inverse Laplace transform of 1/s+5.
Question 6. Find the inverse Laplace transform of 1/( s + 5 ) ( s 2 + 1).
Question 7. The voltage and current in the Laplace domain for a certain system is given by V (s) = 1/12 1/s^2 +3, I(s) = s/s^2+3. Is this system best described as resistive, capacitive, or inductive?
Question 8. The voltage and current in the Laplace domain for a certain system is given by V(s) = 9 1/s^2+16, I(s) = 1/s^2+16. Is this system best described as resistive, capacitive, or inductive?
Question 9. For a second order RLC circuit, in the s-domain s^2 + R/L s + 1/LC = 0. If R = 2 Ω, C = 2 F, and L = 16 H , is the system damped? If so, how? Characterize the behavior of the system.
Question 10. A resistor and inductor are connected in series with a voltage source v ( t ) = 20sin 30t .If R = 12 Ω, L = 4 H, find the total response of the current. Assume there is initially no current. Identify the transient solution.
Provide complete and step by step solution for the question and show calculations and use formulas.