# Vertical format and dotted / double dotted x

1. Jan 13, 2015

### pecchiaw12

1. The problem statement, all variables and given/known data
I am trying to understand what [x^. x^..] means, and information regarding the vertical format it is in .
Can someone please help me understand, or refer me to a website that can aid me. Thank you!

The system is given by

[PLAIN]https://www.physicsforums.com/file:///C:/Users/Guest/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png [Broken] [Broken] and [PLAIN]https://www.physicsforums.com/file:///C:/Users/Guest/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png [Broken] [Broken]

where x is the position and V the voltage across the load resistance.

K= 150000 N/m

D=10 Ns/m

Kt = 0.0728

Ƞ= 50%

R= 19.2 Ω

Rl = 150 Ω

m= my manipulated (independent) variable

2. Relevant equations
[PLAIN]https://www.physicsforums.com/file:///C:/Users/Guest/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png [Broken] [Broken] and [PLAIN]https://www.physicsforums.com/file:///C:/Users/Guest/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png [Broken] [Broken]
3. The attempt at a solution
I believe x^. and x^.. may refer to derivatives and the vertical format may have something to do with vector notation. I just need more specifics if I am to continue my investigation.

#### Attached Files:

• ###### math.docx
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Last edited by a moderator: May 7, 2017
2. Jan 13, 2015

### haruspex

Unfortunately the links to the images appear to be broken, and when viewing the .docx with OpenOffice the expressions appear blank.

3. Jan 13, 2015

### SammyS

Staff Emeritus
Here is the image of the expressions you're wondering about.

From your post I gather that the x with the grave' in the vector should be $\dot{x}$ and $\ddot{x}$, which are time derivatives of position, $x$.

#### Attached Files:

• ###### Vertical.png
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Last edited by a moderator: May 7, 2017
4. Jan 13, 2015

### pecchiaw12

Ok, Thank you. I am beginning to understand. I just need to engage in a bit more self study to understand more of the the mechanics behind the mathematical concepts.

I realize that I was unable to display the equations. In the future, how should I input my formulas to make them visible to others?

5. Jan 14, 2015

### Staff: Mentor

6. Jan 14, 2015

### Ray Vickson

Try LaTeX: if you want to see $\dot{x}$ use the command '\dot{x}' inside the TeX/LaTeX deliminators "# #" (no space) at the start and another pair "# #" (no space) at the end. That will give you an "in-line" formula, as above. To get $\ddot{x}$ just use '\ddot{x}' instead. To get a displayed result, use "[t e x]" (no spaces) at the start and "[/t e x]" (no spaces) at the end. That will give you
$$\dot{x}, \; \ddot{x}$$
Of course, you should also not have the quotation marks " "; I just used these to prevent TeX from trying to process the explanations.

7. Jan 14, 2015

### haruspex

Ray, what about the matrix layout, do you know how to do that?
When I want to use some advanced LaTeX on this forum I have to scratch around to find some prior examples. There does not appear to be any Help button, and when I do web searches for LaTeX the answers I get don't work on this forum, as though there are different versions of LaTeX. Any hints?

8. Jan 14, 2015

### Ray Vickson

You can get
$$\pmatrix{a&b\\c&d}$$ using the command " \p mat rix { a & b \\ c & d } " (no spaces in word pmatrix) or
$$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ using the commands ""\be gin{p matrix} a & b \\ c & d \e nd{p matrix}" (no spaces in command words), although it looks the same; maybe down deep there is some difference between the two. If you want square bracket around your matrix I think you need to input it manually as an array:
$$\left[ \begin{array}{cc}a & b \\ c & d \end{array} \right]$$
Just right-click on the result to see the tex code.

9. Jan 14, 2015

### haruspex

OK, thanks, but what I'm really after is a reference for looking up all the LaTeX controls that work on this forum. As I said, my experience has been that LaTeX code cut and pasted from web pages often doesn't work. E.g. I was trying to make a table yesterday and at http://en.wikibooks.org/wiki/LaTeX/Tables found
\begin{tabular}{ l c r }
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9 \\
\end{tabular}
which, putting in the hashes, produces
$\begin{tabular}{ l c r } 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{tabular}$

10. Jan 14, 2015

### Ray Vickson

I share your desire for such a document. Like you I have found some standard LaTeX constructs that do not seem to work here, at least without some undocumented modifications.

If you want a simple, unbordered table you can input it as an array. I changed the word "tabular" to "array" and got
$$\begin{array}{lcr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}$$

You can put in vertical lines in the usual way, but horizontal lines and solid borders (top and/or bottom) seem to be unavailable. (Side borders using "\le ft[ ... \ri ght]" or "\l eft| ... \ri ght|" seem to work well enough, though. It really would be nice to have a usable table environment here.

$$\left| \begin{array}{l|cr} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right|$$

Last edited: Jan 14, 2015
11. Jan 14, 2015

### haruspex

OK, thanks.

12. Jan 14, 2015

### pecchiaw12

.

#### Attached Files:

• ###### Vertical.png
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13. Jan 14, 2015

### pecchiaw12

would that convert to $\ddot{x}=\dot{x}$, $(15000/m) \dot{x}-(10/m)-(1601.6^2/84.6m)\ddot{x}+1/m=\ddot{x}$ and $V= (240240/169.2)\ddot{x}$

I feel that I have done something wrong in the simplification of the matricies, could somebody assist me in finding my error?

14. Jan 14, 2015

### haruspex

Assuming the image SammyS posted (post #3) is correct, and assuming the vector has $\dot x$ at the top and $\ddot x$ at the bottom (they both look like $\acute x$ to me), then that is a correct expansion. That said, it does look mighty strange. The first equation would lead immediately to $\dot x = Ae^t$.

15. Jan 14, 2015

### pecchiaw12

It is on page 4
http://www.researchgate.net/publication/224505926_Human-powered_small-scale_generation_system_for_a_sustainable_dance_club [Broken]
or
http://ieeexplore.ieee.org/xpl/abst...re.ieee.org/xpls/abs_all.jsp?arnumber=5075243
The Author, Michel Smit, sent me a copy, but I do not want to post it . Because it may cause copyright infringements if I were to do so.

Hopefully this provides more information about where I am coming from, and a greater understanding of the equations at hand.

I am thankful for the help I have already received. Please continue to help me through this predicament.

Last edited by a moderator: May 7, 2017
16. Jan 14, 2015

### pecchiaw12

Once again, this paper has defined the Suspended mass (without dancer)m as 35kg and the estimated mass of the dancer between 70 and 100kg. I wish to find how the Power, Current, and/or Voltage may be affected if the mass of the dancer was higher or lower than estimation (70-100kg).

Is it plausible for me to find this with only the mathematical evidence provided within the document?

17. Jan 14, 2015

### SammyS

Staff Emeritus
Here's an image of the matrix equations directly from the paper authored by Michel Smit.

(The image I posted in Post #3 was from the file attached to the Original Post in this thread.)

Last edited by a moderator: May 7, 2017
18. Jan 15, 2015

### haruspex

Yes, but it seems hard to get accepted when you've not worked in academia since graduating and are no longer associated with an academic institution.
As I wrote, the unbundled equations look remarkably easy to solve.
It looks dubious in other ways... the dimensions don't look right. I can check that more thoroughly if you can tell me what x, m and k (same as K?) represent, what the given units for g mean (radians per metre?). I'm struck in particular by the implication that $\ddot x$ and 1/m must have the same dimensions.

19. Jan 15, 2015

### pecchiaw12

here is some info from post 1 and additional info.

The system is a floor tile that generates electricity when stepped upon.

where x is the position and V the voltage across the load resistance.

k= 150000 N/m The spring coefficient.

D=10 Ns/m Mechanical damping

Kt = 0.0728 Motor constant

g= 22000 rad/m gear ratio it should have been formatted rad/min which is still unconventional and should have been reduced to rad/sec or converted to RPM

Ƞ= 50% Efficiency gears

R= 19.2 Ω Internal resistance motor

Rl = 150 Ω load resistance

m=35 kg Suspended mass (without dancer)

The estimated mass of dancer given is 70-100kg

dotted x would be a time derivative, such as velocity, and double dotted x reprisents a second derivative in respect to time such as acceleration.

If they are velocity and acceleration, then they can be equal if the measurement of time is 1

if d/t=(d/t)/t, d referring to distance, and t, time, and t = 1 then d/1=d/1/1 which simplifies to d=d

this makes sense, but this is only an example I came up with. If it is the correct interpretation (which I doubt) how would the first linear equation be applicable to the rest of this system?

Paulides, J.J.H., J.W. Jansen, L. Encica, E.A. Lomonova, and M. Smit. "Human-Powered Small-Scale Generation System for a Sustainable Dance Club." 2009-EMC-143_revised, 2009, 4.

There, with that citation I should be allowed to post this.

Hopefully this can clear things up a little.

I have also decided using mass as my manipulative variable would result in other variables ( like Resistance) being changed. I asked a friend of mine, and he suggested that I change the gear ratio instead. This seems to make more sense, so I am now trying to find how the power, current, or voltage is affected when the gear ratio is changed.

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20. Jan 15, 2015

### pecchiaw12

If It was wrong of me to post that diagram could someone please notify me.