Sol'n to HW#4

1a) Laplace model:

b) i)

ii)


iii) Is the same as part ii) (sorry!)
i) Laplace model:

Note: we can simplify this slightly by making a couple of source transformations:

Now, we can easily use superposition to find y(t)

Thus,

2a) For t < 0 the capacitor is an open circuit and the inductor acts as a short circuit:

Hence, i_L(0) = 5A and v_c(0) = 0 V. Thus, the frequency domain model for t > 0 is:

Which can be simplified by a couple of source transformations to:

b)