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dean2203

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

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In summary, the conversation is about evaluating the function H(t-8)2cosh(t-8) using the Laplace Transform and the second shift theorem. The proposed solution is 2e^-2s(s/(s^2-1)).

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dean2203

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

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I like Serena

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dean2203 said: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?

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Prove It

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dean2203 said: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.

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

The function H(t-8t)2cosh(t-8) represents the displacement of an object at time t, where H is the initial height, t is the time, and cosh is the hyperbolic cosine function.

To evaluate H(t-8t)2cosh(t-8), you can plug in the given value of t into the function and use a calculator to calculate the hyperbolic cosine value. Then, multiply the result by the initial height H.

The "8t" in the function represents the rate of change of time, meaning the function is dependent on time and how it changes over time. It can also represent the velocity of the object at time t.

Yes, this function can be used to model real-life situations such as the displacement of an object under the influence of gravity or the position of a spring-mass system.

This function can be graphed using a graphing calculator or software. The resulting graph will show the displacement of the object over time. The initial height H will determine the y-intercept, and the rate of change of time will affect the slope of the graph. The function can be interpreted as the position or height of the object at any given time t.

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