Laplace Transform of sinh(at)
The Laplace transform of sinh(at) is a/(s² − a²). See the table rule behind it, then edit the function to transform anything else.
L{sinh(at)} = a/(s² − a²). The hyperbolic pair uses a minus sign: a/(s² − a²).
Use t as the variable. Examples: t^3, e^(-2t), sin(3t), t*cos(2t), 4t^2+3. Write δ(t) as delta(t).
The result
L{sinh(at)} = a/(s² − a²)
Worked example with numbers: L{sinh(2t)} = 2/(s^2 - 4)
- L{sinh(2t)} = 2/(s^2 - 4) Table rule: L{e^(at)sinh(bt)} = b/((s − a)² - b²)
The hyperbolic pair uses a minus sign: a/(s² − a²).
More hyperbolic transforms
Other transforms
Frequently asked questions
What is the Laplace transform of sinh(at)? ▾
L{sinh(at)} = a/(s² − a²). The hyperbolic pair uses a minus sign: a/(s² − a²).
Which rule gives the transform of sinh(at)? ▾
L{e^(at)sinh(bt)} = b/((s − a)² - b²) applied to sinh(2t).
How do I get back from F(s) to f(t)? ▾
Use the inverse Laplace transform. Split F(s) into partial fractions and invert each piece with the same table read backwards — the inverse Laplace transform calculator does this step by step.
About this Calculator
The Laplace transform of sinh(at) is a/(s² − a²). See the table rule behind it, then edit the function to transform anything else.