Few days ago, I saw a beautiful homemade science experiment on Sand Pendulums on Bruce Yeany’s YouTube channel. Go ahead and check it out. It is a cool project to do with your kids.
I will try this experiment with kids during school term holidays around Easter. But first, I wanted to try the simulation in Excel.
Simulating sand pendulum pattern in Excel
Take a look at the final simulation.
Pendulum pattern – Lissajous curve
The patterns generated by sand pendulum are nothing but Lissajous curves. We can generate these curves in Excel by using below equations.
- X = A * SIN(a*t + d)
- Y = B * SIN(b*t)
where
- A & B refer to amplitude (the length pendulum travels before reversing its direction) along X & Y axes
- a & b refer to height of pendulum along X & Y axes (if these are same you get a simple pendulum and thus a straight line pattern)
- d refers to degrees of shift (its a bit complex to explain here, but read about phase shift on Lissajous curve Wikipedia page)
- t refers to radians (degrees).
But this will generate a smooth line, how to show sand?
Simple, after computing each pair of (X, Y) we add a small random noise to them. This creates an impression of sand falling from pendulum on to a surface and bouncing off. Let’s define our new equations as,
- X = A * SIN(a*t + d) + jx * rand()
- Y = B * SIN(b*t) + jy *rand()
Where jx & jy are jitter fractions (very small numbers, lest the dots will be too away from original points)
What if the pendulum never stops?
Since we are simulating the movement of a pendulum in Excel, we can choose to have a never stopping pendulum (ie a simple gravity pendulum). In this case A & B values never change.
In real life, A&B will reduce with each oscillation until the pendulum comes to a stop (because there is air drag, friction and other forces at play too).
Let’s look at the chart & VBA
Enough physics & maths. Let’s take a look at the chart & VBA behind this simulation.
- Set up 3 columns, one with t values starting from 0 and increasing by 0.05 per cell, next two with X & Y values.
- Leave the X&Y values blank. We will use VBA to fill these.
- Let’s say we use 5000 (x,y) values to plot the chart. This gives enough variation. You can alter the number of rows later.
- Create a scatter plot with smoothed line using these 5000 (x,y) values.
- Using VBA, iterate thru column t and calculate X & Y values for each t value using above equations.
- Update the chart by using doEvents after every n calculations. Try n=25 first and change as you see fit. Updating the chart after every calculation slows down the animation significantly.
- Change A, B, a, b, d, jx, jy and air drag factors to generate different curves.
Here is the VBA code used for the animation.
Sub animate()
Dim xVal As Double, yVal As Double, jx As Single, jy As Single
Dim t As Range
Dim a1 As Single, drag As Single
Dim a2 As Double, b2 As Double, d As Double
Dim updateScreen As Integer
Dim tVals As Range
a1 = 1
drag = Range("air.drag")
a2 = [a.2]
b2 = [b.2]
jx = [j.x]
jy = [j.y]
d = WorksheetFunction.pi() / Range("d")
Set tVals = Range("t.vals")
Range(tVals.Offset(, 1), tVals.Offset(, 2)).ClearContents
Range("done") = "drawing..."
For Each t In tVals
xVal = a1 * Sin(t * a2 + d) + jx * Rnd()
yVal = a1 * Sin(t * b2) + jy * Rnd()
t.Offset(, 1).Value = xVal
t.Offset(, 2).Value = yVal
'update screen after every 25 times this loop has run
updateScreen = IIf(updateScreen = 25, 0, updateScreen + 1)
If updateScreen = 0 Then DoEvents
'Reduce A & B values by using drag
a1 = a1 * (1 - drag)
Next t
Range("done") = "done"
End Sub
Download Pendulum Sand Patterns Workbook
Click here to download the Pendulum Sand patterns workbook. Play with the animate & random pattern buttons to see some cool patterns.
Have you done this experiment?
This is a cool way to teach kids the awesome pattern power of simple things in life. Have you done this experiment? If not, give it a try. If you think playing with sand is too messy, try the Excel workbook.
Also check out: 3D dancing pendulums post to see some cool & clever animations. Huge collection of spreadsheet tools & simulations for teachers.
17 Responses to “Budget vs. Actual Profit Loss Report using Pivot Tables”
Good Work, Yogesh & Chandoo! Thanks.
Hi everybody,
first sorry I am late to say something about this topic;actually I was waiting last part
second I am not accountant I am an Engineer
third """"Very Important""" the idea is not about Loss but I am sure it is profit
Based on third it shows:
1- How to use EXCEL
2- How to use pivot TABLES
3- How to collect and arrange DATA
4- How to make reports
Many Thanks
Hi Yogesh and Chandoo,
Thank you for sharing your knowledge!
You guys are great!
thanks chandoo and yogesh, thanks for you lessons, are great!....i have a idea for a budget. I try to do it..... thanks for all
Thanks a lot for sharing the most powerful tool worldwide "knowledge"
Warm greetings from Peru
Hi -
This is a really great article because it's a simple and common thing you'd want to do with a pivot table but not at all obvious how to do it! So - muchas gracias to Chandoo and Yogesh!
One thing - I couldn't get past the group error in the sample file. I would click on ungroup but it didn't seem to have any effect. I'd appreciate it if anybody has any pointers here.
-Juanito
Hi Chandoo
I am also having the group error. Can't seem to ungroup? Appreciate if you explain further on the steps required in order to get to calculated items.
Many thanks and keep up the great work.
Cheers
Adam
Hi Chandoo,
I'm struggling resolving the problem depicted below:
I have a set of data, with (among others) a "Region" field (can be APJ, EMEA, or AMS), and a "Country" field.
Unfortunately, I need to group data by the following 4 Regions: APeJ, Japan, EMEA and AMS.
I first tried to make a pivot with Region and Country in the rows (or columns), and then group Country data as per the above.
Alas, as soon as I have a new Country that appear in my data set, my groupings are broken, and I have to redo the job of ungrouping, grouping etc.
I thought I could try to use calculated item, by adding first a new column to my dataset concatenating Region_Country, and create an "APeJ" calculated item that would sum all the "APJ_*" and substract the "APJ_Japan", but again, no clue, as I can't find a way to use any wild card in those formulas.
Given that I already found extremely helpful tips and tricks in your site that helped me manage that bunch of data, I'm pretty sure you'll have a bright idea on how I can solve that one!
Thanks in advance for your lights!
Hi Catherine...
In such cases, I advice using an additional column in the data itself. You can set-up a grouping table else where with country in first column, region in second column. And then in the data, you can add an extra column and use VLOOKUP to fetch the region based on the country.
Then feed this entire data (with extra column) to pivot table and use the extra column to group the data.
Hi Chandoo,
Thank you for your prompt answer.
I finally came to the same conclusion - after a rest 🙂 . I was probably too tired Friday evening (it was rather late), having spent hours in manipulating all my surveys data so as to pull rolling averages, make nice graphs and so on, and was trying to find a complex solution when there was a simple one.
Thanks again,
Catherine
Hey,
Great post!
I for example have different database structure with the following fields :
Date, Expense, Income, Sum (Income - Expense), Category (Sales, Cost of Goods and etc).
Creating a P&L report for the whole year works great. Including gross margin % and etc.
Though, creating P&L report by QTR/Month is becoming impossible since i get the following error : “This PivotTable report field is grouped. You cannot add calculated item to grouped filed.”
Is there a solution for this kind of problem?
Like Adam and Juanito, I also cannot ungroup.
Would appreciate it if you can add a few more lines and a screenshot or two on where to put the mouse cursor to ungroup.
Hi, I have figured out the ungrouping problem. One of the earlier steps was to group by month, if you pull the month back down to the column then right click and then select ungroup, then pull the month back up so you end up with just data source and budget/actual as the headings, then you can continue on.
To solve the ungroup problem, my method is:
Copy the "data" sheet to a whole new Excel workbook
and directly work on Part 6.
And since it is a fresh copy, Excel don't show me the "can't ungroup" problem. Hope this help.
Thank you Yogesh for this wonderful tutorial.
Kent, Malaysia
Just when i thought pivots were awesome i learn about inserting the calculated fields and that makes them more awesome. chandoo where have you been all my life.
Hello - your P&L pivot version has really impressed my boss and would like to use it. I have applied it for a actual vs budget vs forecast model I have created. One problem. In your variance above the operating profit percent % variance shows 33.8% but I want it to show (0.01) point or the true diff from prior budget.
I know I can add calculation to the side but boss would like to see it in pivot table.
Please help
Thanks
I have a further query which may solve my above dilemma. Is it possible to add a column that calculates percent increase. So in the example above a new column would be added to show variance %.
Any help would be appreciated.
Thanks