Laplace Transform of t·cos(at)

The Laplace transform of t·cos(at) is (s² − a²)/(s² + a²)². See the table rule behind it, then edit the function to transform anything else.

L{t·cos(at)} = (s² − a²)/(s² + a²)². L{t·cos(at)} = (s² − a²)/(s² + a²)².

f(t) — the function to transform

Use t as the variable. Examples: t^3, e^(-2t), sin(3t), t*cos(2t), 4t^2+3. Write δ(t) as delta(t).

Try an example

The result

L{t·cos(at)} = (s² − a²)/(s² + a²)²

Worked example with numbers: L{t·cos(3t)} = (s^2 - 9)/(s^2 + 9)^2

L{t·cos(3t)} = (s^2 - 9)/(s^2 + 9)^2 Table rule: L{t·cos(bt)} = (s² − b²)/(s² + b²)²

L{t·cos(at)} = (s² − a²)/(s² + a²)².

More products transforms

L{t·e^(at)} L{t²·e^(at)} L{e^(at)·sin(bt)} L{e^(at)·cos(bt)} L{t·sin(at)}

Other transforms

L{1} L{t} L{t²} L{t³} L{t⁴} L{e^(at)}

Frequently asked questions

What is the Laplace transform of t·cos(at)? ▾

L{t·cos(at)} = (s² − a²)/(s² + a²)². L{t·cos(at)} = (s² − a²)/(s² + a²)².

Which rule gives the transform of t·cos(at)? ▾

L{t·cos(bt)} = (s² − b²)/(s² + b²)² applied to t·cos(3t).

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.

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