Harrington Ross
02/06/2023 · High School
\( L \{ \cosh 3 t \} \)
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Step-by-step Solution
To find the Laplace transform of \( \cosh(3t) \), we can use the formula for the Laplace transform of \( \cosh(at) \), which is given by:
\[ L\{ \cosh(at) \} = \frac{s}{s^2 - a^2} \]
In this case, \( a = 3 \), so the Laplace transform of \( \cosh(3t) \) is:
\[ L\{ \cosh(3t) \} = \frac{s}{s^2 - 9} \]
Therefore, the Laplace transform of \( \cosh(3t) \) is \( \frac{s}{s^2 - 9} \).
Quick Answer
The Laplace transform of \( \cosh(3t) \) is \( \frac{s}{s^2 - 9} \).
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