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For this video Lego sent me some of their Saturn V rocket sets.
But this isn't a video about space - I actually want to talk about the physics of how to keep
tall things from shaking, like how to keep skyscrapers from swaying too much in the wind,
or in an earthquake.
The taller something is, the more liable it is to sway back and forth, so to demonstrate
this, the Saturn V seemed by far like the best and coolest Lego set for the job (even
if not the most realistic).
If you don’t your tall thing to sway, either because you’re worried it’ll fall apart
or you’re worried it’ll freak out the people inside, you could just make it stiffer
– either by adding more stuff or using more rigid materials – this isn’t always the
most elegant solution, and gets expensive fast.
But there’s another, clever solution.
From a physics perspective, a tall thing like a building is really an upside-down pendulum
- when it gets bent a little bit to one side, the building’s natural stiffness pulls it
back the other way, and so on.
And there's a neat phenomenon that happens with pendulums when you attach two of them
together with a spring: they start swapping energy back and forth – first one oscillates,
then both together, then the other has all the oscillations, then the first again, and
so on.
The same thing happens with solid blocks and springs, too, or any two oscillating things
that are coupled together.
In a perfect frictionless simulation this energy swapping will go on forever.
But in the real world there's friction and air resistance and the spring itself might
heat up, causing the objects to lose energy, and the oscillations dampen over time.
And this phenomenon is what you can use to ‘discourage’ your upside-down pendulum
from shaking in ways you don’t want it to.
A big tall object is going to want to sway back and forth at its own natural frequency
of swaying (which depends on its height, weight, and stiffness).
If you then attach a smaller object to it that can sway to and fro, and add a little
bit of friction, then any time the big object trades its energy to the little object, the
little object loses the energy to friction rather than trading it back to the big object,
and this dampens out the big object's oscillations.
In practice, you normally put the little object inside the big object, which looks more like
this, but the principle is the same.
And you don’t want to use just any old little object and any old spring.
It turns out that for a particular big thing, there’s an optimal combination of weight
and friction and spring strength for the little object.
And only with your setup perfectly tuned will you get the fastest possible loss of energy
and the best slowing down of the shaking.
That’s why this setup is called a “tuned mass damper” – “damper” because it
dampens the swaying, and “tuned” because the little object is specifically tuned to
steal energy from this particular big thing’s natural tendency to swing.
Which brings us to the Lego Saturn V rockets: in one of the rockets I’ve put a weighted
pendulum in the place the lunar module should go, while the other just has the weights stuck
in place.
If all goes well, and if I’ve done my math right, then when I bump the table, the rocket
with the pendulum should sway a lot less than the rocket without.
As you can see, the tuned mass damper does actually help! (though it’s a bit subtle).
Here’s a graph of the motion of the rocket in each case, which makes it more obvious.
And though tuned mass dampers definitely weren’t used in the saturn V rocket in this way (since
this is where the lunar module went), they are used in skyscrapers and even in other
things that aren’t buildings (though they’re usually hard to notice).
For example, if you look closely at power lines, a lot of them have this little dumbbell
thing on them, which is a tuned mass damper that keeps the lines from shaking too vigorously
in the wind.
And tuned mass dampers have been used to reduce unwanted vibrations in airplane engines, formula
1 racing cars, and audio speaker cones.
So there you go – the tuned mass damper, aka the physics of how to use little things
to stop big things from shaking!
As you've probably guessed by now, this video was sponsored by LEGO - I've been a huge fan
of LEGO for pretty much my entire life, spending hours and hours building and rebuilding all
sorts of LEGO projects as a child and teenager, and even more recently sneaking some into
MinutePhysics videos.
So I'm excited that LEGO wanted to full-on sponsor a video.
The Saturn V sets are super cleverly designed and really fun to build, and of course I'm
a big Apollo fan and I love how the rocket actually stages like the real thing.
Anyway, the folks at LEGO want me to point you to their online and physical stores which,
naturally, have the largest collection of lego sets, and also allow you to find and
buy individual pieces a la carte for custom projects, get expert lego help, and with LEGO
VIP you can get early access to new LEGO sets.
Thanks so much to LEGO for sponsoring this video and filling my childhood with creative
delight.