## Introduction: The Pendulum Wave

👷Sometimes, physics can be used to create beautiful art. And it's really cool to watch. Kinetic art is art that relies on motion to achieve a specific effect. Often that motion is just an application of simple laws of physics. Waves and harmonic motion (some examples include pendulums and springs) are often great sources of inspiration for creating mesmerizing displays.

In this project, you will use the laws ofsimple pendulum motion to create a “pendulum wave apparatus”: a device where many

pendulums of different lengths (and therefore different periods) start swinging at the same time. As they move in and out of sync, the

pendulums create a sequence of cycling visual wave patterns.

✨__NOTE__--> We will make this physics apparatus in just __6__ simple steps. After when it's done it not only used for physics stuff, but a home🏡 decorative piece that can be used to amaze people,because of its looks.if you are Keen to watch science education videos🎥, check out my YouTube channel science mode laboratory ]

## Supplies

**Wood**

- 1.2 cm thickness, 77 inch long and 36 inch wide plywood, you can use any wood but, make sure the thickness from 1.2 cm to 3 cm.

**Hardware **

- M12(12mm) hex nut, such as This(the bigger the Nut," better because of mass)

- 2.2 cm long and small diameter nails for joining plywood.

**Materials**

- Nylon Beading Thread, such as This (any thread will work only make sure it is not too stretchy.

- Pushpins, such asThis

- transparent tape

- super glue

- pencil

- Measuring centimetre scale

- Measuring Measurement inch Tape, such as This

**Necessary Tools **

- drill machine

- Hand-Held Circular wood cutting Saw, such as This

- Hammer

## Step 1: Cutting the Plywood

I started out by cutting plywood board that was 77 inch(1.9558 metre) long and 36 inch(0.9144 metre) wide.thickness 1.2 cm.

For making frame we need to cut 4 same size Planks for legs that were 17 inches long and 1.2 inch wide, And only one board for for top section, that was 30 inches long and 1.2 inch wide.

Also cut a 24.5 inches long and 2 inches wide plywood section from remaining cutted plywood, For swinging the pendulums.

## Step 2: Making the Side Legs of Frame

For building the side legs of frame we have to join plywood board that we have cut.

1. Take one 17 inch board and join with 30 inch board by applying glue and nails as shown in above images.

2. Now take one more 17 inch board and join to other side of 30 inch board, by applying glue and nails(as shown images).

3. After joining the ply-board it will look like the last image in above.

## Step 3: Joining Other Side Legs

For joining other side legs the two 17 inch board

Should be connected opposite to previous joined legs.(reference-above images)

1. First apply glue and join 17 inch board to upper side of previous joined board by nails as shown in the above pictures.

2. Do same for one last left 17 inch board.

3. After it's done it will look like last image in above. now wait for for atlest 12 hours for the glue to harden.

### Attachments

## Step 4: Drill Holes and Insert Pushpins

We are drilling holes and inserting Pushpins because we have to hang pendulums on it.(reference above images)

1. Mark a gap of 1.5 inches on top section of board. Drill 17 pushpins pilot holes evenly(1.5 inch) spaced along the length of top section of board.

I decided I wanted 16 pendulums in this array and however, many pendulums you would like you just need to have one more pushpin than the total number pendulums.

2. After drilling pilot holes Insert pushpins.

## Step 5: Now Let's Do Some Mathematics

__NOTE__- Skip this step if you don't want to get into maths.read step6 you will be fine.

Or, **"lets do maths" **→→→↓↓📑

When all pendulums are swinging they form all sorts of pattern like double helixes, triple helixes and spirals.But actually you need a very specific curve that can be determined with some maths.this is the equation to use in order to define the the length of each pendulum.

L = g[Tmax/2π(k+n+1)]^2

…... Tmax is for overall cycle length in second. L stands for length(in meters), g stands for gravity,we have π = 3.14.now n a pretty easy number to figure out that stands for the number of Pendulum that are on the array,so if we wanted to calculate the length of the second pendulum we put 2 in for n. if you wanted to calculate the length of third we put 3 and so on........

The last variable is K and we actually don't know what this number is, we have to solve for this number based on the length of the very first pendulum in the series so in order to solve for k we just need to decide the length for my first pendulum and input that measurement in metre.

1. So my first pendulum in the array is 0.23 metre then input 9.8m/s for gravity, 2 times of π we put 1 for n because we are working on the very first pendulum in the series and I decided on a 24 second duration(Tmax). By solving it we get k= 23.

=> 0.23=9.8[24/6.28(k+1+1)]^2__k = 23__

2. Now put the value of k in equation and replacing n with all the numbers 2 to through 16 we can solve L the length of each of those individual pendulums.

L = 9.8[24/6.28(k+2,3,4,......+1]^2

So, i have 16 pendulums in this array,so this are the outputted numbers for all the lengths of my various pendulum down the line.↓ __**(In Meters)***__

0.23 metre

0.211m.

0.196m.

0.183m.

0.170 m.

0.159m.

0.149m.

0.140m

0.131m

0.124m

0.117m

0.110m

0.105m.

0.099m

0.094m

0.089m__**In Centimetre***__

23cm, 21.1cm, 19.6cm,18.3cm,17cm, 15.9cm,14.9cm,14cm,13.1cm,12.4cm,

11.7cm,11cm,10.5cm, 9.9cm, 9.4cm,

8.9cm

~ Using the this equation.

L = g[Tmax/2π(k+n+1)]^2

you can make a pendulum wave of any size by replacing the variable 'L' with the desired length of your longest pendulum when calculating the variable 'K'. Once K has been determined for that starting length Just replace the variable 'n' with the number 2 through however many more pendulums you would like in the series and calculate L for each of them.

📐The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. Two pendula with different masses but the same length will have the same period. Two pendula with different lengths will different periods; the pendulum with the longer string will have the longer period.

## Step 6: Hang the Pendulums to Frame

I chose jewelry nylon beading thread you can use any thread(make sure it is not too stretchy and soft).

1. The nuts can easily be hung in the array by first feeding them onto a length of string.each nut can be hung from the frame by twisting the string around the pushpins📌 and pressing the pin tightly to secure the string in place. (Reference above images.)

2. Measure the string by cm scale like in the above images.i am not measuring each pendulum from where the pins but rather from where the string is contacting the top board relying on the corner of the board to be the top of the pendulums.

__NOTE__-Here are the measurement I used, starting with the longest pendulum and moving throughout the shortest.__**In Centimetre*__

23cm, 21.1cm, 19.6cm,18.3cm,17cm, 15.9cm,14.9cm,14cm,13.1cm,12.4cm,

11.7cm,11cm,10.5cm, 9.9cm, 9.4cm,

8.9cm.

=> Just hang the pendulums by this measurement For reference about how to hang pendulums refer upper images in __step6__.

Apply tape or hot glue for correct measurement.

## Step 7: Swinging and Seeing Different Patterns

With the help of previously cutted 24.5 inches plywood swing the pendulums.

And enjoy the beautiful patterns.

## Step 8: Going Further

You can modify the apparatus to add more pendulums or create a longer cycle than 24 seconds. The trick is to first decide how long

you want the overall cycle to be (we used 24 seconds in this design, but it can be as long as you like)

Participated in the

Made with Math Contest