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2. The following initial value problem describes oscillatory motion in a viscous medium: + 26 + w y = 0; 11(0) = 0, y'(0) = '00 (2) where b, w, and 00 are real, positive, constants. a) If the dimensions of y and t are length (L) and time (T), respectively, what are the dimensions of w, b, and '00? Express your answer in terms of products LaTb, where a and b are rational numbers. b) Show that y(t) = Acos(wt) + B sin(wt) is a solution to (2) when b = 0. What are the values of A and B? c) Starting with y(t) = e)\" (where A is, in general, a complex number), nd the solution to (2). You must show all the steps leading to the solution. d) What are the values of w and b, if the period of oscillation in the viscous medium is 5 s and in the absence of the viscous medium (b = 0) is 3s