Kinetic/Potential Energy in Waves

[Kosta1234]

Homework Statement

Hi,
I'm stuck on some question..
There are given to waves in the following equation:

The question asks to find the energy density of them, and after it to find the kinetic and the potential energy in t = 2.5 seconds.

V = | 2 | [m/s]
T = 4 [N]
p (density) = 1 [KG/M]

Homework Equations

The Attempt at a Solution

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to find the energy density I used this equation:

the solution to this equation (that equals to energy density) is:

then, I've set in place t = 2.5, and the energy density is equal to:

which is great. but my problem is to find the kinetic and the potential energy in t = 2.5 seconds.
I've not understood this question well.
I can find the TOTAL energy by using integral of the energy density to 'dx'.
How can I find the specific kinetic or potential energy?

Thanks.​

 

[haruspex]

There are probably standard equations, but from first principles...
Consider an element length dx. You know its mass and you know its speed as a function of x and t, etc.

 

[Kosta1234]

Do you mean to Integrate the density to dx?
but I don't know it's length it's infinite.

 

[haruspex]

Do you mean to Integrate the density to dx?
but I don't know it's length it's infinite.

The total energy will be infinite, but you are asked for the mean energy density. What length do you need to encompass to assess that?