Transfer Function

Please help in understanding how to solve the following problems.

1. The impulse response for a circuit is h(t) = e^-t, t >= 0. What is the response function of the circuit in the s-domain if the input is f(t) = cos(2t)?

2. The transfer function for a circuit is H(s) = 1/[(s+2)(s+5)]. What are the poles? Is this an impulse response stable circuit?

3. The transfer function for a circuit is H(s) = 1/[(s-2)(s+5)]. What are the poles? Is this an impulse response stable circuit?

4. Suppose that H(s) = (s+4) / [(s+4)^2 + 49]. What is the natural response of the circuit?

5. If H(s) = (s+4) / [(s+4)^2 + 49], is the circuit impulse stable?

6. If H(s) = (s-4) / [(s-4)^2 + 49], is the circuit impulse stable? What is the natural response?

7. Consider a series RLC circuit with R = 2 Ohm, C = 1/2 F, and L = 4 H. The initial voltage across the capacitor is 2 V and the initial current flowing in the circuit is zero amps. Find the voltage across the capacitor in the s domain and determine if the circuit is stable.

8. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series to the load. What is the impedance of the load? Use phasor transform methods to obtain your answer.

9. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series to the load. What is the current flowing through the load? Use phasor transform methods to obtain your answer.

10. A load has a 20 ohm resistor and a 4 Henry inductor connected in series. It is connected to a power source with v(t) = 100 cos(50t), connected in series with the load. What is the average power delivered to the load?