Instructions: Write up neat, organized solutions to ALL problems ON YOUR OWN. Be sure to include acknowledgment of anyone who you worked with or received help from.
Problem 1 For what positive values of b do. y°(t) + by'(t) + 4y(t) = 0 have solutions that are overdamped oscillators? Explain.
Problem 2 An inductor (L =1 II) and resistor (R = 0.1 Ohms) are joined in series with a voltage source with E(t) = 10 — 2t volts. If there is no current at time t = 0, find an expression for the current in the circuit at time t. Hint: Go back to the handout on circuits. Which variable is used to denote the current? What is the relevant differential equation for the cumnt?
Problem 3 Find the inverse Laplace Transforms, by manipulating the functions to match a form in our table.
(a) Y(,) = — rft (b) Y(s) (,t1) ‘2F4 (c) Y(s) =