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Several problems in electricity

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See attached for full description of problems.

1. Determine the Laplace transform of ?(t) = + 5e^-4t + 12sin 3t.
2. If v(t) = 10e^-t/3 for some circuit, when does the voltage fall to 37% of its initial value?
3. Let ?(t) = sin2t. What is the Laplace transform of d? / dt ?
4. The charge in a certain capacitor varies as q = 20e^-4t sin 2t C. What is the voltage if the capacitor is 2 F?
5. The charge in a certain inductor varies as q = 2 sin 2t C. What is the voltage if the inductance is 2 H?
6. The current flowing through a 1 H inductor is 10 cos 20t amps. Find the voltage.
7. The current flowing through a 2 F capacitor is i(t) = 5 cos 2t amps. What is the voltage?
8. The current flowing through a 2 H inductor is i(t) = 5 cos 2t amps. What is the voltage?
10. What is the energy in a 2 F capacitor if v(t) = cos2t at t = pi seconds?
11. What is the energy in a 10 H inductor if i(t) = cos2t at t = pi seconds?
12. What kind of damping is associated with ? (t) =(A + Bt) e^wt?

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