Intgration of a harmonic function help please

In summary, the conversation discusses the integration of a function and the power of omega in the solution. The conversation explains that when doing a change of variable in the integral, one omega in the denominator cancels out with one of the two omegas in the numerator, resulting in the RHS only containing omega to the power of 1. However, the original poster is confused about the presence of both h and w in cos(hwt) and questions whether the power of w and h should be equal. It is clarified that when integrating over the whole period, the power of omega should be to the power of 2, not 1.
  • #1
lordcx
3
0
intgration of a function*** help please***

actually this is not a homework, I found this explanation in a journal paper but I could not understand it. Can someone give me an explanation or possibly a proof that:


Homework Statement



if:
e;x}=\sqrt{2}\sum_{h=1}^{H}h\omega&space;V_{h}cos%28h\omega&space;t+\frac{\pi&space;}{2}%29.png


then why integration over whole period is:
t%29}{\mathrm{d}&space;t}&space;\right&space;%29^{2}dt=\omega&space;\sum_{h=1}^{H}h^{2}V_{h}^{2}.png



Homework Equations



I have problem with the power of omega, my solution returns w with power 2, while the power of omega in answer is one, Can someone help me for the reason?
 
Last edited:
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  • #2


Well, when you do a change of variable in the integral in the LHS, one omega pops up in the denominator, canceling one of the 2 from the numerator. That's why the RHS contains omega only to the power 1.
 
  • #3


bigubau said:
Well, when you do a change of variable in the integral in the LHS, one omega pops up in the denominator, canceling one of the 2 from the numerator. That's why the RHS contains omega only to the power 1.

thank you, but as you see cos(hwt) contains both h and w. means by changing the variable the power of w and h should be equal. I'm confused:cry:

png.png


and over whole period:

png.png


then we will have

png.png


not

png.png


am I wrong??
 
Last edited:

FAQ: Intgration of a harmonic function help please

What is a harmonic function?

A harmonic function is a type of function in mathematics that satisfies Laplace's equation, which states that the second partial derivatives of the function with respect to its variables must equal zero. In simpler terms, a harmonic function is one that is smooth and balanced, with no areas of rapid change or extreme values.

Why is it important to integrate a harmonic function?

Integrating a harmonic function can help us solve problems in physics and engineering, as many physical systems can be modeled using harmonic functions. It also allows us to understand the behavior of these functions and make predictions based on their properties.

What are the methods for integrating a harmonic function?

There are several methods for integrating a harmonic function, depending on the specific function and its properties. Some common methods include using the fundamental theorem of calculus, integration by parts, and trigonometric substitutions.

What are some real-world applications of integrating a harmonic function?

Integrating harmonic functions can be applied to various fields, such as electromagnetism, fluid dynamics, and signal processing. For example, in electromagnetism, we can use integration to calculate the electric potential of a system, which is a harmonic function.

Are there any tips or tricks for integrating a harmonic function?

One tip for integrating a harmonic function is to first identify any symmetries or patterns in the function, as this can often simplify the integration process. It is also helpful to have a solid understanding of basic integration techniques and to practice solving problems to improve your skills.

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