Exercise · ZW-INVERSE-LAPLACE-TRANSFORM-010 · ★★★ Advanced
What is \(\mathcal L^{-1}\left\{\dfrac{1}{s^2(s+1)}\right\}\)?
Choose one option.
Show answer
- D. \(t-1+e^{-t}\)
Explanation
Partial fractions: \(\frac1{s^2(s+1)}=\frac1{s^2}-\frac1s+\frac1{s+1}\), whose inverse is \(t-1+e^{-t}\).
Review the concept: Inverse Laplace transform
The inverse transform \(\mathcal L^{-1}\) of a function \(F(s)\) is the function \(f(t)\), defined for \(t\ge0\), whose Laplace transform is \(F(s)\).
\[f(t)=\mathcal L^{-1}\{F(s)\}\iff \mathcal L\{f\}=F\]
More practice problems: inverse laplace transform
- ZW-INVERSE-LAPLACE-TRANSFORM-001 What is mathcal L^-1\1s-4\?
- ZW-INVERSE-LAPLACE-TRANSFORM-002 What is mathcal L^-1\(5)/(s^2+25)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-003 What is mathcal L^-1\(s)/(s^2+9)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-004 What is mathcal L^-1\(6)/(s^4)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-005 What is mathcal L^-1\(1)/(s(s+1))\?
- ZW-INVERSE-LAPLACE-TRANSFORM-006 What is mathcal L^-1\(2s+3)/(s^2+4)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-007 What is mathcal L^-1\(1)/(s^2+2s+5)\?
- ZW-INVERSE-LAPLACE-TRANSFORM-008 What is mathcal L^-1\(s+2)/((s+1)(s+3))\?