Laplace Transform of 2sin(3t) + 4cos(3t)
The Laplace transform of 2sin(3t) + 4cos(3t) is 6/(s^2 + 9) + 4s/(s^2 + 9). See the table rule behind it, then edit the function to transform anything else.
L{2sin(3t) + 4cos(3t)} = 6/(s^2 + 9) + 4s/(s^2 + 9). A sinusoid at a single frequency always lands over the same denominator 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{2sin(3t) + 4cos(3t)} = 6/(s^2 + 9) + 4s/(s^2 + 9)
- L{2·sin(3t)} = 6/(s^2 + 9) Table rule: L{e^(at)sin(bt)} = b/((s − a)² + b²)
- L{4·cos(3t)} = 4s/(s^2 + 9) Table rule: L{e^(at)cos(bt)} = (s − a)/((s − a)² + b²)
A sinusoid at a single frequency always lands over the same denominator s² + a².
More combinations transforms
Other transforms
Frequently asked questions
What is the Laplace transform of 2sin(3t) + 4cos(3t)? ▾
L{2sin(3t) + 4cos(3t)} = 6/(s^2 + 9) + 4s/(s^2 + 9). A sinusoid at a single frequency always lands over the same denominator s² + a².
Which rule gives the transform of 2sin(3t) + 4cos(3t)? ▾
L{e^(at)sin(bt)} = b/((s − a)² + b²) applied to 2·sin(3t); L{e^(at)cos(bt)} = (s − a)/((s − a)² + b²) applied to 4·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.
About this Calculator
The Laplace transform of 2sin(3t) + 4cos(3t) is 6/(s^2 + 9) + 4s/(s^2 + 9). See the table rule behind it, then edit the function to transform anything else.