Laplace Transform of Constant Multiple/Examples/Example 1

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

\(\ds \laptrans {\sin 3 t}\)

\(=\)

\(\ds \dfrac 1 3 \dfrac 1 {\paren {s / 3}^2 + 1}\)

Laplace Transform of Constant Multiple, Laplace Transform of Sine

\(\ds \)

\(=\)

\(\ds \dfrac 3 {s^2 + 9}\)

simplification

$\blacksquare$

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Important Properties of Laplace Transforms: $4$. Change of scale property