Inverse Laplace Transform of s/(s² + 4)²
The inverse Laplace transform of s/(s² + 4)² is 1/4t·sin(2t). See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.
L⁻¹{s/(s² + 4)²} = 1/4t·sin(2t). The classic resonance response t·sin(2t)/4.
e.g. 2s+3
Expanded or factored, e.g. (s+1)(s^2+4)
The result
L⁻¹{s/(s² + 4)²} = 1/4t·sin(2t)
Partial fractions: s/(s^2 + 4)^2
- Invert s/(s^2 + 4)^2 — L⁻¹{s/(s² + b²)²} = t·sin(bt)/(2b)
The classic resonance response t·sin(2t)/4.
More inverse transforms
Frequently asked questions
What is the inverse Laplace transform of s/(s² + 4)²? ▾
It is f(t) = 1/4t·sin(2t). The classic resonance response t·sin(2t)/4.
What are the partial fractions here? ▾
F(s) splits into s/(s^2 + 4)^2, and each piece is inverted separately.
How can I check this answer? ▾
Transform 1/4t·sin(2t) forward again with the Laplace transform calculator — you should get back s/(s² + 4)².
About this Calculator
The inverse Laplace transform of s/(s² + 4)² is 1/4t·sin(2t). See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.