Respuestas - Sección 4.5.1

Aquí encontrarás las respuestas a todos los ejercicios de la sección 4.5

1. $\hspace{0.5cm} \dfrac{1}{s^2}e^{-4s}$
2. $\hspace{0.5cm} \dfrac{1}{s+2}e^{-2s}$
3. $\hspace{0.5cm} \dfrac{s}{s^2+4}e^{-\pi s}$
4. $\hspace{0.5cm} -\dfrac{s}{s^2+1}e^{-\frac{\pi}{2}s}$
5. $\hspace{0.5cm} \dfrac{1}{2}\left(\mathrm{t-2}\right)^2\mu\left(t-2\right)$
6. $\hspace{0.5cm} sen\left(t-\pi\right)\mu\left(t-\pi\right)$
7. $\hspace{0.5cm} cos{2}\left(t-\dfrac{\pi}{2}\right)\mu\left(t-\dfrac{\pi}{2}\right)$
8. $\hspace{0.5cm} \mu\left(t-1\right)-e^{-\left(t-1\right)}\mu\left(t-1\right)$
9. $\hspace{0.5cm} -\mu\left(t-2\right)-\left(t-2\right)\mu\left(t-2\right)+e^{\left(t-2\right)}\mu\left(t-2\right)$
10. $\hspace{0.5cm} \dfrac{1}{s^2}-\dfrac{1}{s^2}e^{-2s}-\dfrac{2}{s}e^{-2s}$
11. $\hspace{0.5cm} \dfrac{1}{s}-\dfrac{1}{s}e^{-4s}+\dfrac{1}{s}e^{-5s}$
12. $\hspace{0.5cm} \dfrac{2}{s^3}e^{-s}+\dfrac{2}{s^2}e^{-s}+\dfrac{1}{s}e^{-s}$
13. $\hspace{0.5cm} \dfrac{1}{s^2+1}-\dfrac{1}{s^2+1}e^{-2\pi s}$
14. $\hspace{0.5cm} y(t)=5e^{-t}+\dfrac{3}{2}\left[e^{-\left(t-\pi\right)}-sen\left(t-\pi\right)+cos{\left(t-\pi\right)}\right]\mu\left(t-\pi\right)$
15. $\hspace{0.5cm} y(t)=5\mu\left(t-1\right)-5e^{-\left(t-1\right)}\mu\left(t-1\right)$
16. $\hspace{0.5cm} y(t)=\dfrac{1}{4}-\dfrac{1}{4}cos{2}t-\dfrac{1}{2}sen2t-\left[\dfrac{1}{4}-\dfrac{1}{4}cos{2}\left(t-1\right)\right]\mu\left(t-1\right)$
17. $\hspace{0.5cm} y(t)=cos{2}t+\left[\dfrac{1}{3}sen\left(t-2\pi\right)-\dfrac{1}{6}sen2\left(t-2\pi\right)\right]\mu\left(t-2\pi\right)$