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# Transfer functions and steady state

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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=2ohms, c=.5F, and L=4H 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.