How to calculate Laplace transform using table: Trigonometric Function sin(3t)

Consider the trigonometric function sin(3t). Find its Laplace transform using the table of common Laplace transforms.

In a previous exercise, we calculated the Laplace transform of a sine function using the definition. In this post, we will use the table to solve the above exercise!

Solution:

Line 3 from the transform table tells us:

\displaystyle\mathscr{L}\{\sin(bt)\}=\frac{b}{s^{2}+b^{2}}

So, for b=3 , we have:

\displaystyle \mathscr{L}\{\sin(3t)\}=\frac{3}{s^{2}+3^{2}}

which yields:

\displaystyle \mathscr{L} \{\sin(3t)\}=\frac{3}{s^{2}+9}

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