Problem

(a) Sketch the time functions given.(i) 2e–3t u(t – 5)(ii) –2e–3t u(t – 1)(iii) –5e–atu(t...

(a) Sketch the time functions given.
(i) 2e–3t u(t – 5)
(ii) –2e–3t u(t – 1)
(iii) –5e–atu(t – b)
(iv) –Ke–c(t–a) u(t – b)
(b) Use Tables to find the Laplace transforms.

	F(s)		ROC
1. δ (t)	1		All s
2. u (t)			Re(s) > 0
3. t			Re(s) > 0
4. tn			Re(s) > –a
5. e-at			Re(s) > –a
6. te-at			Re(s) > –a
7. tn e-at			Re(s) > 0
8. sin bt			Re(s) > 0
9. cos bt			Re(s) > –a
10. e-at sin bt			Re(s) > –a
11. e-at cos bt			Re(s) > 0
12. t sin bt			Re(s) > 0
13. t cos bt
Name		Property
1. Linearity, (7.10)
2. Derivative, (7.15)
3. n th-order derivative, (7.29)
4. Integral, (7.31)
5. Real shifting, (7.22)
6. Complex shifting, (7.20)
7. Initial value, (7.36)
8. Final value, (7.39)
9. Multiplication by t, (7.34)
10. Time transformation,
11. Convolution
12. Time periodicity