# need help with evaluating H(t-8t)2cosh(t-8)

#### dean2203

##### New member
need help with evaluating H(t-8t)2cosh(t-8)

#### Klaas van Aarsen

##### MHB Seeker
Staff member
need help with evaluating H(t-8t)2cosh(t-8)
Hi dean,
What do you want to evaluate exactly?
Did you try substituting t=0?
Do you know what the function H is?
Btw, is there perchance a typo? Can it be that the first factor should be H(t-8) instead?

#### Prove It

##### Well-known member
MHB Math Helper
need help with evaluating H(t-8t)2cosh(t-8)
Hi Dean, this is Hayden, I'm assuming that you want to do a Laplace Transform of this. In future please post the ENTIRE question.

I also expect it was $\displaystyle \mathcal{L}\left\{ H \left( t - 8 \right) \cdot 2\cosh{ \left( t - 8 \right) } \right\}$.

Use the second shift theorem.

\displaystyle \begin{align*} \mathcal{L}\left\{ H\left( t - 8 \right) \cdot 2\cosh{ \left( t - 8 \right) } \right\} &= 2\,\mathrm{e}^{-2\,s} \,\mathcal{L} \left\{ \cosh{ \left( t \right) } \right\} \\ &= 2\,\mathrm{e}^{-2\,s}\left( \frac{s}{s^2 - 1} \right) \end{align*}