Respuestas - Sección 4.5.1

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

  1. 1s2e−4s\hspace{0.5cm} \dfrac{1}{s^2}e^{-4s}

  2. 1s+2e−2s\hspace{0.5cm} \dfrac{1}{s+2}e^{-2s}

  3. ss2+4e−πs\hspace{0.5cm} \dfrac{s}{s^2+4}e^{-\pi s}

  4. −ss2+1e−π2s\hspace{0.5cm} -\dfrac{s}{s^2+1}e^{-\frac{\pi}{2}s}

  5. 12(t−2)2μ(t−2)\hspace{0.5cm} \dfrac{1}{2}\left(\mathrm{t-2}\right)^2\mu\left(t-2\right)

  6. sen(t−π)μ(t−π)\hspace{0.5cm} sen\left(t-\pi\right)\mu\left(t-\pi\right)

  7. cos2(t−π2)μ(t−π2)\hspace{0.5cm} cos{2}\left(t-\dfrac{\pi}{2}\right)\mu\left(t-\dfrac{\pi}{2}\right)

  8. μ(t−1)−e−(t−1)μ(t−1)\hspace{0.5cm} \mu\left(t-1\right)-e^{-\left(t-1\right)}\mu\left(t-1\right)

  9. −μ(t−2)−(t−2)μ(t−2)+e(t−2)μ(t−2)\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. 1s2−1s2e−2s−2se−2s\hspace{0.5cm} \dfrac{1}{s^2}-\dfrac{1}{s^2}e^{-2s}-\dfrac{2}{s}e^{-2s}

  11. 1s−1se−4s+1se−5s\hspace{0.5cm} \dfrac{1}{s}-\dfrac{1}{s}e^{-4s}+\dfrac{1}{s}e^{-5s}

  12. 2s3e−s+2s2e−s+1se−s\hspace{0.5cm} \dfrac{2}{s^3}e^{-s}+\dfrac{2}{s^2}e^{-s}+\dfrac{1}{s}e^{-s}

  13. 1s2+1−1s2+1e−2πs\hspace{0.5cm} \dfrac{1}{s^2+1}-\dfrac{1}{s^2+1}e^{-2\pi s}

  14. y(t)=5e−t+32[e−(t−π)−sen(t−π)+cos(t−π)]μ(t−π)\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. y(t)=5μ(t−1)−5e−(t−1)μ(t−1)\hspace{0.5cm} y(t)=5\mu\left(t-1\right)-5e^{-\left(t-1\right)}\mu\left(t-1\right)

  16. y(t)=14−14cos2t−12sen2t−[14−14cos2(t−1)]μ(t−1)\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. y(t)=cos2t+[13sen(t−2π)−16sen2(t−2π)]μ(t−2π)\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)