root mean square question..

[nabliat6]

calculate the RMS (root mean square) of this function.
https://i50.tinypic.com/2iuq80x.jpg
the period T=4
the formula is

[latex]V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V_r^2dt}[/latex]
[latex]V_{rms}=\frac{1}{4}4\int_{0}^{T}(4t)^2dt}[/latex]
[latex]V_rms=\sqrt{s}=\sqrt{\frac{16}{3}}[/latex]
the solution says that they divide the graph into 4 triangles
and they sum their areas

but they dont use the integral?
why they say (4t)^2
from where the 4t comes from?

why they say that its the root of the area
why they dont divide by the period?

 

[BrownOut]

They don't use the integral becuas it's not a well behaved function. It's easier to just use triangles. If you used an integral, you'd have to integrate over each linear portion and them sum the results of the integrations. I dont know the answer to the rest of your questions.

 

[MrAl]

calculate the RMS (root mean square) of this function.
https://i50.tinypic.com/2iuq80x.jpg
the period T=4
the formula is

[latex]V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V_r^2dt}[/latex]
[latex]V_{rms}=\frac{1}{4}4\int_{0}^{T}(4t)^2dt}[/latex]
[latex]V_rms=\sqrt{s}=\sqrt{\frac{16}{3}}[/latex]
the solution says that they divide the graph into 4 triangles
and they sum their areas

but they dont use the integral?
why they say (4t)^2
from where the 4t comes from?

why they say that its the root of the area
why they dont divide by the period?

Hi there,


When you ask a question like this you have to be very careful how you ask it and how you type your text.
For example, it looks like you wanted to type V sub r but where did that come from?
Also, you have typed one closing bracket but no open bracket. Where is the open bracket?
Also, you said that they are NOT using the integral, yet you said that they used "(4t)^2", so how
could they have used (4t)^2 if they didnt use the integral?

You should probably go over this and ask the question again in a different way.
I suspect that you might be asking how to get the rms value without using the integral, but cant be
sure until you verify this stuff.

Try restating the question and maybe even posting more from where this question came from.


ADDED:
This makes a little sense if you think first that they wanted to imply that the triangles all have a slope
of 4 or -4, and they wanted to say that you can add the areas ABOVE each triangle, but then you would
have to divide by the square root of 3 to get the right answer. That also implies however that they graph
they drew was not done that accurately, as the time values and amplitude values would not look that
unusually spaced. That would mean the "4t" was to imply that each triangle has a slope of 4 or -4, and
the period of EACH triangle was 1 for a total period of 4 as they state.