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A pendulum when reaching the extremes stands still for a moment, allowing us to see the details of the bob, and gradually increase its velocity towards the equilibrium point. Therefore, its trace of trajectory is blurred in our eyes.

Long-exposure can portray the trajectory, but not the detail of the bob: enter image description here Time lapse, on the other hand, shows too much detail that the trace of trajectory isn't portrayed: enter image description here

This one is closed to what I'm looking for, but it's not in direct view. The transition is not really smooth.

enter image description here

This one is closer, but it only shows the bob once, not in both extremes like the previous. The trajectory is also faded.

enter image description here

Q: How to portray these in one image:

  • The details of the bob only at both extremes,

  • The blurred trace of trajectory,

  • The smooth transition in between? Bonus if it can show the gradualism of the velocity.

I can edit existed images/video or setup things.


FYI: Interesting related phenomenon: Persistence Of Vision

  • @Gerhardh Please see: Short answers as comments — please resist the urge As short as it is, your comment has a the kernel of a very good answer! – Michael C Dec 12 '17 at 7:51
  • Not an answer (because an existing one has already said everything I might say that answers the question), but an observation: The reason the next to last image is not smooth is probably due to a flickering lighting source, such as standard fluorescent bulbs. If one knew the frequency of the lights and had high enough resolution to count the 'steps', one could compute the exposure time. – Michael C Dec 12 '17 at 7:57
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    Is the first photo even an image of a pendulum trajectory? It looks parabolic, or perhaps a catenary (hanging cable), rather than circular arc. – scottbb Dec 12 '17 at 12:49
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    @scottbb it's from The Pendulum Project. It's actually a special kind of pendulum, and is captured from the beneath – Ooker Dec 12 '17 at 13:50
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    Ah, it's a Lissajous figure. It's showing the "ground track", the path of oscillating in 2 dimensions projected onto the normal plane. I suggest that the image is misleading to your goal, because it doesn't capture the same information / viewpoint as the other images. – scottbb Dec 12 '17 at 14:34
28

Let's look at the last picture.

  • If you want a black background, you need to be careful not to spill light. It's relatively easy to control in a large studio, it's almost impossible in a small room. You need a background which is far away. You could even shoot outside at night if the weather allows it.

  • You need some continuous light to show the trajectory. Note that the pendulum spends more time on the extreme than at the bottom of the trajectory because it's standing still at the extremes and fastest at the bottom. That's why the trajectory seems faded. You could put your continuous source of light closer to the bottom to mitigate that effect.

  • To show frozen detail on the pendulum, you could manually trigger the flash when the pendulum is at both extremes. The period of the pendulum is constant and only depends on the length of the string, so you could tap your feet to the "rhythm" and pop the flash when needed. Bert Stephani and David Hobby call it BioWizard sync.

So you could try:

  • Very dark environment, except for one continuous light close to your pendulum.
  • Launch the pendulum.
  • ISO 200, f/10, begin 10 second exposure.
  • Get the rhythm, pop flash manually once at both extremes.
  • Wait for the exposure to finish.
  • Try again with different parameters until it looks good to you. No Photoshop needed!

Here's a related example I took a few years ago.

  • Long exposure on a tripod
  • 1 red LED on the nose of the skateboard
  • 1 blue LED on the tail
  • 1 slide in the middle to reverse the direction of the skateboard
  • 1 manual flash trigger during the slide

enter image description here

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    There's an interesting electronics/sensing project to be done in automating the flash triggering if you haven't got a good enough sense of rhythm (which of course depends on the pendulum length. – Chris H Dec 12 '17 at 9:39
  • First, it's possible (even likely) that most of those are blended photos with multiple shots being used for for the final, For example one of the pendulum still at each end, and one of the pendulum in motion. Second, you could use a laser trigger to catch the flash at the pause point. The Pluto Trigger is one that I've been keeping my eye on, is reasonable in price and comes with a laser trigger. – Hughman Dec 15 '17 at 3:53
5

I wonder what would happen if, in addition to the steps offered by this excellent answer, you would use a long enough exposure (say 5-10 minutes) for the length of the pendulum's travel to decay appreciably while using a very dim constant light source? (Or even two, one from above and one from below so that you could flag both of them from shining towards the background.)

You would need to do both of your flash 'pops' as soon as possible after opening the shutter. Perhaps get synced to the rhythm of the pendulum before opening the shutter. That way you capture the bob with the two flash bursts at the very extremes of the arc of travel recorded in the long exposure.

As the pendulum's arc decays, the bob would spend more and more time closer to the center of the arc as it ceases to spend any more time on the ends. The period of oscillation remains constant, but the distance travelled decreases which means the speed through the bottom of the arc would also be decreasing. This might help equalize the brightness of the blurred trail in the middle compared to the extremes.

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    Interesting idea. Controlling the spill with a 5 min exposure would be really hard though. – Eric Duminil Dec 12 '17 at 8:22
  • @EricDuminil It's easy. Angle the lights towards areas beyond the edges of the FoV and use flags to block spill within the FoV. Or just use snoots pointed at angles away from the background. You'd obviously want to shoot in an area that could be totally dark except for your lighting, but that's what a studio should allow you to do. – Michael C Dec 12 '17 at 8:32
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    Might be a good application of the Live Time mode on Olympus cameras... – junkyardsparkle Dec 12 '17 at 20:05
  • It also just occurred to me that this might be a good case for using blacklights and a fluorescent pendulum. That could make it much easier to keep a black background. – junkyardsparkle Dec 12 '17 at 23:47
5

Consider adding a light source to the bob itself, such as an LED. Set your exposure for several periods of the pendulum, and flash your external light source at the extremes. This attached light source should trace a clear path, and the flashes should illuminate the extremes.

LEDs are fairly directional, so you should be able to control how much light leaks onto the bob. The LED can be powered by a small battery attached to the bob, or fed through the pendulum's cable

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    And to address the "bonus" question of portraying acceleration, you could have one LED shining downward onto a small dangling "tassle" that would change its angular relationship to the pendulum depending on speed... :) – junkyardsparkle Dec 12 '17 at 20:01
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Your problem, in reality, is a bit more technical than it looks at first glimpse.

It seems you need these specific requirements:

The exposure should reflect the velocity, so at point (1) it should look less bright because is passing faster, ant point (2) should be brighter, because it is moving slower, and you want to see the object clearly in (3) at the extremes.

enter image description here

Let us address point 1 and 2.

You do not want to use a single source of light at the center because you will have a hotspot at the center canceling the "speed" effect. This light will expose more at the center if it is either far enough or big enough. (Probably one big diffuse light can work)

enter image description here

What I recommend is that you exaggerate this speed effect using two lateral lights.

So the effect is more visible because you will have a bot more light when the pendulum is at the extremes.

enter image description here

But here is the real technical problem.

To expose exactly the object at the edges you probably need a light sensor trigger, probably an infrared one so this light does not add to the photo.

enter image description here

But you can overcome it in several ways.

Manually triggering a flash at the extremes (I then recommend a soft trigger, probably using remote triggers like Yongnuo 603 which is really cheap) because the built-in button on a flash, the test button usually is hard to press, for safety reasons)


I would not recommend a very long exposition for one reason, it probably can detect the decay of several passes, increasing exposure at the center. Of course, this decay depends on how massive is the pendulum.

Try to limit this exposition to 2-3 passes only, so do not use very dim lights.

Some lights can have a flicker effect, so take that into account.

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  • I don't see the necessity for two lights, as your problem with the single light is only relevant if the light is at or below the arc of the pendulum. Lighting it from the front would eliminate this problem. If placed at a far enough distance from the pendulum, it will produce fairly even lighting over the entire arc. – Robin Jan 15 '18 at 22:32
  • I mentioned "(Probably one big diffuse light can work)" – Rafael Jan 23 '18 at 19:07
1

If you want to have an image of a single swing to represent the velocity and trajectory, I would make a small adjustment to @Eric excellent answer.

Use a flash with second curtain sync, so you can eliminate any 'extra' exposure to the continuous light by stopping the exposure when you hit the starting point in the swing. The manual flash trigger would only be needed for the apex farthest from the start of the swing. This would give a more even light distribution to match the swing. A random exposure time means the pendulum will be exposed for the duration of the exposure, and thus appear brighter in any parts of it's trajectory that is exposed more (within reason, a very long exposure time as @Michael Clark suggested would effectively eliminate this effect)

For example, if the exposure stops when the pendulum is halfway through it's swing, and resulted in the first half of the swing being exposed for twice as long as the second half, this will be noticeable in the resulting image. The more swings, the lesser the effect, but it also means you will see the decay of the swing, which I assume you don't want. If you do, then follow Michael's advice.

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1

For a software answer as opposed to all of the excellent photographic answers I would suggest taking a high resolution video of a well lit pendulum through at least 1 full cycle.

You can then split the video into frames, (I would use Image Magic convert for this), ensure that you have an equal number of frames of each point in the cycle and then exposure blend, (Hugin), but with multiple copies of the two end images, a little playing about should get the results you need. Where the pendulum is moving fastest it will be dimmest.

Both ImageMagick & Hugin are free, gratis & open source and available for most platforms.

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