Sin Function Data Analysis
 

Hi,
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

Thanks!

Sin Function Data Analysis
 

In case this helps, here is also a sample of my data. It is one column:

-16.8229
-13.4258
-3.7614
7.8206
16.1112
17.4997
11.3897
0.587
-10.0967
-15.8696
-14.1202
-5.6565
5.5832
14.5154
17.2058
12.6234
2.7443
-8.0242
-14.8725
-14.5632
-7.3823
3.3322

Sin Function Data Analysis
 

You will have to do better than that to get homework help.
If you plot the data (XY plot) you will see a sine wave.
Were the measurements made every second, every 1/10 of second.....?
What exactly do you want to find - the length of the pendulum, the value of
g ?
You have not given us enough data.
The sine function in Excel is =SIN(A1) bit if A1 has degrees you need
=SIN(RADIANS(A1))
best wishes
--
Bernard Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme



"Matt" wrote in message
...
Hi,
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

Thanks!

Sin Function Data Analysis
 

When you are replying to a message, remember to quote enough of the original
message to put your new contribution into context.

In this case, your original question was:
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

One option is to put your data values in column B. Put a set of dependent
variables in column A, say 0 to 21 in your case.
You could then put a sine wave equation in say column F, using a formula
=C$24*SIN(PI()*(A1-D$24)/E$24), using constants in C24:E24.
You can put an error squared term in column G, with the formula =(F1-B1)^2,
and then sum the error squared terms with =SUM(G1:G22)

You can then use Tools/ Solver to minimise this last term by changing
C24:E24, but you may need a reasonable guess at the values initially to
allow it to converge, so you'll probably need to look at the form of the
data to guess those initial values.

It's probably useful to plot the original data and your sine-wave
approximation together on a chart to see how well you've done.
--
David Biddulph

"Matt" wrote in message
...
In case this helps, here is also a sample of my data. It is one column:

-16.8229
-13.4258
-3.7614
7.8206
16.1112
17.4997
11.3897
0.587
-10.0967
-15.8696
-14.1202
-5.6565
5.5832
14.5154
17.2058
12.6234
2.7443
-8.0242
-14.8725
-14.5632
-7.3823
3.3322

Sin Function Data Analysis
 

What i'm looking to find is an equation that models the data so i can put
that equation into matlab. I know the length of the pendulum, g, etc., and
each set of data is taken every 1 cylce- the time measurements arent
significant for right now. What I mean't more was a trendline- for charts, i
know that you can create a linear regression, or "best fit" line and show the
equation. I am looking to do something like this, but for a sine curve. any
ideas? thanks!

matt

"Bernard Liengme" wrote:

You will have to do better than that to get homework help.
If you plot the data (XY plot) you will see a sine wave.
Were the measurements made every second, every 1/10 of second.....?
What exactly do you want to find - the length of the pendulum, the value of
g ?
You have not given us enough data.
The sine function in Excel is =SIN(A1) bit if A1 has degrees you need
=SIN(RADIANS(A1))
best wishes
--
Bernard Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme



"Matt" wrote in message
...
Hi,
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

Thanks!

Sin Function Data Analysis
 

also in regards to the data, the data is measured in degrees offset from the
resting position. heres the data again:

-16.8229
-13.4258
-3.7614
7.8206
16.1112
17.4997
11.3897
0.587
-10.0967
-15.8696
-14.1202
-5.6565
5.5832
14.5154
17.2058
12.6234
2.7443
-8.0242
-14.8725
-14.5632
-7.3823
3.3322

Sin Function Data Analysis
 

What functions or equations ......can I use to find the sin function

representing this pendulum using my data?


Just a note. Notice that the average value of your data is -0.690127
This showed up in the Fourier analysis also.
With enough sampling, and at proper spacing, I would expect an average closer to 0.
(The highest frequency term I show is -0.584582 (-1)^x, which I think means your data has a lot of "noise," or the accuracy of the measurements is not really out to 0.0001.)
I may be wrong, but just my guess.
--
Dana DeLouis


"Matt" wrote in message ...

What i'm looking to find is an equation that models the data so i can put
that equation into matlab. I know the length of the pendulum, g, etc., and
each set of data is taken every 1 cylce- the time measurements arent
significant for right now. What I mean't more was a trendline- for charts, i
know that you can create a linear regression, or "best fit" line and show the
equation. I am looking to do something like this, but for a sine curve. any
ideas? thanks!

matt

"Bernard Liengme" wrote:


You will have to do better than that to get homework help.
If you plot the data (XY plot) you will see a sine wave.
Were the measurements made every second, every 1/10 of second.....?
What exactly do you want to find - the length of the pendulum, the value of
g ?
You have not given us enough data.
The sine function in Excel is =SIN(A1) bit if A1 has degrees you need
=SIN(RADIANS(A1))
best wishes
--
Bernard Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme



"Matt" wrote in message
...

Hi,
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

Thanks!

Sin Function Data Analysis
 

"best fit" line ...for a sine curve. any

Hi. I might be wrong, but I get about

-17.136457630408 * Sin(0.89542489309982 + 0.680013434718991 * x)

Different methods arrive at slightly different solutions, but they appear to all agree with a freq of about 0.68.
Of course, your data shows an offset from the start .(0.89..)

Just for fun. Not what you wanted, but if you wanted to Curve fit your data with just Sin, you could phase the Sin & Cos frequencies together with a phase shift via the Fourier Transform.
This will reproduce your data.
However, from inspection, this does not work for what you want because the data is not periodic at the end points.. Your ending data point does not complete a cycle.
Therefore, this will just reproduce your data.
The equation has been arranged by the Abs( ) maximum value of each frequency component. We note that they all appear to be important for accuracy.
Note that with an even number of data points, the highest frequency cancels the Sin function, and the remaining Cos function just alternates (+-) and hence is changed to (-1)^x

Sub Demo()
Dim n
Dim x
Dim Pi
Pi = WorksheetFunction.Pi

For x = 0 To 21
n = -0.690127272727273 _
- 0.584581818181818 * (-1) ^ x _
- 12.8103481758612 * Sin(0.565539827065221 - (2 * Pi * x) / 11#) _
+ 8.56499995503438 * Sin(2.98941440438005 + (3 * Pi * x) / 11#) _
- 3.83348772011928 * Sin(1.00524778699338 - (Pi * x) / 11#) _
- 3.41877601052572 * Sin(3.01947952790798 - (4 * Pi * x) / 11#) _
- 2.30614951785526 * Sin(2.76357456361827 - (5 * Pi * x) / 11#) _
- 1.75316017345818 * Sin(2.5352536449401 - (6 * Pi * x) / 11#) _
- 1.48203251984954 * Sin(2.33432031961824 - (7 * Pi * x) / 11#) _
- 1.32029235196495 * Sin(2.13811691588771 - (8 * Pi * x) / 11#) _
- 1.22360877020275 * Sin(1.94568189061646 - (9 * Pi * x) / 11#) _
- 1.1768369078447 * Sin(1.75967181016055 - (10 * Pi * x) / 11#)

Cells(x + 1, 2) = n
Next x
End Sub

--
HTH :)
Dana DeLouis


"Matt" wrote in message ...

What i'm looking to find is an equation that models the data so i can put
that equation into matlab. I know the length of the pendulum, g, etc., and
each set of data is taken every 1 cylce- the time measurements arent
significant for right now. What I mean't more was a trendline- for charts, i
know that you can create a linear regression, or "best fit" line and show the
equation. I am looking to do something like this, but for a sine curve. any
ideas? thanks!

matt

"Bernard Liengme" wrote:


You will have to do better than that to get homework help.
If you plot the data (XY plot) you will see a sine wave.
Were the measurements made every second, every 1/10 of second.....?
What exactly do you want to find - the length of the pendulum, the value of
g ?
You have not given us enough data.
The sine function in Excel is =SIN(A1) bit if A1 has degrees you need
=SIN(RADIANS(A1))
best wishes
--
Bernard Liengme
Microsoft Excel MVP
http://people.stfx.ca/bliengme



"Matt" wrote in message
...

Hi,
I currently have a set of data for a pendelum, resembeling a sin function.
What functions or equations in excell can I use to find the sin function
representing this pendelum using my data?

Thanks!