Using the Laplace transform pairs of Table 2.1 and the Laplace transform theorems of Table 2.2, derive the Laplace transforms for the following time functions:

a. e^-atsin ωt u(t)

b. e^-atcos ωt u(t)

c. t³u(t)

Table 2.1:

Table 2.1:

TABLE 2.1 Laplace transform table Item no. F(s) 1. 8(t) 1 1 u(t) 1 3. tu(t) n! 4. t"u(t) 5. e-dl'u(t) s+a 6. sin tu(t) s2 + ? 7. cos otu(t) 2.