L Eo R FIGURE 4.3.10 Circuit in Problem 35 36. Use the Laplace transform to find the charge q(t) RC-series when q(0) = 0 and E(t) = Eve , k > 0. Con two cases: k # 1/RC and k = 1/RC. 4.3.2 Translation on the t-axis In Problems 37-48, find either F(s) or f(t), as indicated. 37. L{ (t - 1) u (t - 1) } 38. Pez -' ou (t - 2) } 39. Litu(t - 2) } 40. 2{ (3t + 1) u (1 - 1) } 41. L {cos 2t U(t - TT) } 42. L{ sin tou (t - T/2) } 43 . SP e 1 1 ( 1 + e - 25 ) 2 ] $ 3 s + 2 e TT S Se TTS/2 45 . Se 46. P- $ 2 52 + 4 - S -2s e 47. 2 5(5 + 1) ) 48. 2 153 (5 - 1)) In Problems 49-54, match the given graph with one of the functions in (a)-(f). The graph of f(t) is given in FIGURE 4.3