How to calculate Laplace transform using table: Trigonometric Function cos(4t)

Consider the trigonometric function cos(4t). Find its Laplace transform using the table of common Laplace transforms.

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

Solution:

Line 4 from the transform table tells us:

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

So, for b=4 , we have:

\displaystyle \mathscr{L}\{\cos(4t)\}=\frac{s}{s^{2}+4^{2}}

which yields:

\displaystyle \mathscr{L} \{\cos(4t)\}=\frac{s}{s^{2}+16}

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