Laplace Transform of 5e^(-2t)·sin(4t)
The Laplace transform of 5e^(-2t)·sin(4t) is 20/((s + 2)^2 + 16). See the table rule behind it, then edit the function to transform anything else.
L{5e^(-2t)·sin(4t)} = 20/((s + 2)^2 + 16). The classic underdamped step response term in control systems.
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{5e^(-2t)·sin(4t)} = 20/((s + 2)^2 + 16)
- L{5·e^(-2t)·sin(4t)} = 20/((s + 2)^2 + 16) Table rule: L{e^(at)sin(bt)} = b/((s − a)² + b²)
The classic underdamped step response term in control systems.
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Frequently asked questions
What is the Laplace transform of 5e^(-2t)·sin(4t)? ▾
L{5e^(-2t)·sin(4t)} = 20/((s + 2)^2 + 16). The classic underdamped step response term in control systems.
Which rule gives the transform of 5e^(-2t)·sin(4t)? ▾
L{e^(at)sin(bt)} = b/((s − a)² + b²) applied to 5·e^(-2t)·sin(4t).
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 5e^(-2t)·sin(4t) is 20/((s + 2)^2 + 16). See the table rule behind it, then edit the function to transform anything else.