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