Laplace Transform of t·sin(at)
The Laplace transform of t·sin(at) is 2as/(s² + a²)². See the table rule behind it, then edit the function to transform anything else.
L{t·sin(at)} = 2as/(s² + a²)². Differentiating the transform in s: L{t·sin(at)} = 2as/(s² + a²)².
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{t·sin(at)} = 2as/(s² + a²)²
Worked example with numbers: L{t·sin(2t)} = 4s/(s^2 + 4)^2
- L{t·sin(2t)} = 4s/(s^2 + 4)^2 Table rule: L{t·sin(bt)} = 2bs/(s² + b²)²
Differentiating the transform in s: L{t·sin(at)} = 2as/(s² + a²)².
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Frequently asked questions
What is the Laplace transform of t·sin(at)? ▾
L{t·sin(at)} = 2as/(s² + a²)². Differentiating the transform in s: L{t·sin(at)} = 2as/(s² + a²)².
Which rule gives the transform of t·sin(at)? ▾
L{t·sin(bt)} = 2bs/(s² + b²)² applied to t·sin(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 t·sin(at) is 2as/(s² + a²)². See the table rule behind it, then edit the function to transform anything else.