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Laplace Transform

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There may be a few characters missing in the questions below but this is what should be used to come up with answers.

1) Determine the Laplace transform of f(t) = +5e^-4t + 12sin 3t.

2) If the voltage across a 2 F capacitor is initially zero, what is the instantaneous power if the current is A?

3) The charge in a certain inductor varies as q = 2 sin 2t C. What is the voltage if the inductance is 2 H?

4) The current flowing through a 2 F capacitor is i(t) - 5 cos 2t amps. What is the voltage?

5) The voltage across a 2 F capacitor is v = 20e^-4t volts. What is the instantaneous power?

6) What kind of damping is associated with f(t) = (A+Bt) e^wt?

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