Laplace Transform of Constant Multiple/Examples/Example 1

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Examples of Use of Laplace Transform of Constant Multiple

Let $\laptrans f$ denote the Laplace transform of the real function $f$.


$\laptrans {\sin 3 t} = \dfrac 3 {s^2 + 9}$


Proof

\(\displaystyle \laptrans {\sin 3 t}\) \(=\) \(\displaystyle \dfrac 1 3 \dfrac 1 {\paren {s / 3}^2 + 1}\) Laplace Transform of Constant Multiple, Laplace Transform of Sine
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 3 {s^2 + 9}\) simplification

$\blacksquare$


Sources