What happens inside a mechanical metronome when you move the block to change its tempo?
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A mechanical metronome is based on a pendulum. Pendulums have a quirk where the *period* (how long it takes to swing back and forth) doesn’t change with how far it’s going, but how heavy the pendulum is and where the weight is relative to the fulcrum.
This happens because if the pendulum starts from a higher point, it will accelerate and go faster all the way down, but then it’ll swing up higher and take longer to slow down on the other side. If it starts from a lower point, it’ll swing more slowly, but with less momentum it won’t go up as high so it’ll slow down, stop, and reverse direction faster. These two things perfectly balance, so that no matter how *far* the pendulum is swinging, it will always take exactly the same amount of time to swing back and forth.
However, mass takes longer to accelerate and longer to slow down, so a heavier pendulum will have a longer period. And, the further the weight is from the point of rotation – the fulcrum – the more angular momentum it will have so it’ll take longer.
A mechanical metronome is a swinging pendulum with a small electromagnet that gives it just a tiny little push with every swing – just enough to keep it swinging for as long as the battery still has power. Since we can’t change the timing of the metronome by pushing it farther, we need to either adjust how much weight there is, or move the weight closer or farther from the fulcrum. And, indeed, the latter is what you’re doing when you adjust the weight. You’re moving it closer or farther from the fulcrum, changing the angular momentum and thus changing how long the period will be.
This stability with pendulums is why large clocks use them for keeping time. You can carefully tune the pendulum by adjusting the weight at the end up or down until the pendulum is swinging at exactly once per second, or twice per second, or once per two seconds…whatever the gears in the clock are designed for. The pendulum keeps going with the help of either a wound up spring or a weight inside the clock that pulls on some gears as it slowly falls. When the spring or the weight have run out of energy, you wind it up again.
Of course, in both the metronome and the clock, when you add energy back in it forces the pendulum to move just a little faster than it normally would, which changes the timing very slightly. That’s fine, you adjust the pendulum accordingly to make up for that. However, when the battery or spring is running low, the nudge it gives will be smaller and the metronome or clock will also move just a little slower, throwing off the time by a tiny big. You probably won’t notice at all with a metronome, but with a clock running for days and weeks and months, that little discrepancy adds up and you need to occasionally adjust the time on the clock to keep it correct.
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