Publicado en por Edison Del Rosario

Transformada de Laplace – Tabla

Referencia: Lathi Tabla 4.1 p334. Oppenheim Tabla 9.2 p692. Hsu Tabla 3-1 p115

No. x(t) X(s) ROC
1a δ(t) 1 Toda s
1b δ(t-T) e-sT Toda s
2a μ(t) 1s\frac{1}{s} Re{s}>0
2b -μ(-t) 1s\frac{1}{s} Re{s}<0
3 tμ(t) 1s2\frac{1}{s^2} Re{s}>0
4a tnμ(t) n!sn+1\frac{n!}{s^{n+1}} Re{s}>0
4b tn−1(n−1)!μ(t) \frac{t^{n-1}}{(n-1)!} \mu (t) 1sn\frac{1}{s^n} Re{s}>0
4c −tn−1(n−1)!μ(−t) -\frac{t^{n-1}}{(n-1)!} \mu (-t) 1sn\frac{1}{s^n} Re{s}<0
5 eλtμ(t) 1s−λ\frac{1}{s-\lambda} Re{s}>0
6 teλtμ(t) 1(s−λ)2\frac{1}{(s-\lambda)^2} Re{s}>0
7 tneλtμ(t) n!(s−λ)n+1\frac{n!}{(s-\lambda)^{n+1}}
8a cos (bt) μ(t) ss2+b2\frac{s}{s^2+b^2} Re{s}>0
8b sin (bt) μ(t) bs2+b2\frac{b}{s^2+b^2} Re{s}>0
9a e-atcos (bt) μ(t) s+a(s+a)2+b2\frac{s+a}{(s+a)^2+b^2} Re{s}>-a
9b e-atsin (bt) μ(t) b(s+a)2+b2\frac{b}{(s+a)^2+b^2} Re{s}>-a
10 μn(t)=δnδtnδ(t)\mu_n (t) = \frac{\delta ^n}{\delta t^n} \delta (t) sn Toda s
11 μ−n(t)=μ(t)⊛...⊛μ(t) \mu_{-n} (t) = \mu (t) \circledast \text{...} \circledast \mu (t)

n veces

 1sn\frac{1}{s^n} Re{s}>0
12a re-atcos (bt+θ) μ(t) (rcos⁡(θ)s+(arcos⁡(θ)−brsin⁡(θ))s2+2as+(a2+b2)\frac{(r\cos (\theta)s + (ar \cos (\theta) - br \sin (\theta))}{s^2+2as+(a^2+b^2)}
12b re-atcos (bt+θ) μ(t) 0.5rejθs+a−jb+0.5re−jθs+a+jb\frac{0.5 re^{j \theta}}{s+a-jb} + \frac{0.5 re^{-j \theta}}{s+a+jb}
12c re-atcos (bt+θ) μ(t) As+Bs2+2as+c \frac{As+B}{s^2+2as+c}
r=A2c+B2−2ABac−a2r = \sqrt{\frac{A^2 c +B^2 -2ABa}{c-a^2}} θ=tan⁡−1(Aa−BAc−a2) \theta = \tan ^{-1} \Big( \frac{Aa-B}{A\sqrt{c-a^2}}\Big)

b=c−a2 b = \sqrt{c-a^2}
12d e−at[Acos⁡(bt)+B−Aabsin⁡(bt)]μ(t) e^{-at}\Bigg[A \cos (bt) + \frac{B-Aa}{b} \sin (bt) \Bigg] \mu (t) As+Bs2+2as+c\frac{As+B}{s^2 + 2as+c}
b=c−a2 b = \sqrt{c-a^2}

Transformada Laplace – Tabla de Propiedades

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