Saramsha

No. 023  ·  9 October 2026

Push With It, Not Against It

A swing has a rhythm of its own, set by nothing but its length. Push at any other rhythm and your effort mostly fights itself; push at exactly that rhythm and tiny shoves pile up into a wide arc. Drag the push-rate slider slowly from one end to the other and watch the curve below trace itself out.

right now rates you've already tried the swing's own rhythm

About this piece

Every swing already knows its own rhythm

Let a swing hang still and nudge it once. It falls back, overshoots the other way, falls back again — and the time that one full there-and-back takes depends on almost nothing except how long the ropes are. Not how hard you nudged it, not how heavy the rider is: a longer swing is slower, a shorter one is quicker, and that is nearly the whole story. This is the swing's natural rhythm, and the simulation above fixes it at a little under half a push every second, so a full back-and-forth takes about two and a half seconds.

Now push it repeatedly, a small shove each time, and ask what happens to the energy you are putting in. If your pushes land at a rate that has nothing to do with that natural rhythm, they arrive at essentially random points in the swing's cycle — sometimes helping it along, sometimes shoving against the direction it is already moving, cancelling out roughly as much as they add. The swing settles into a small, steady wobble no matter how hard each individual push is, because the pushes are not cooperating with each other. Push at the natural rhythm instead, and every single shove lands while the swing is already moving the way you're pushing it. Nothing cancels. Each push adds a little more energy on top of the last, and the arc grows — not because any one push is stronger, but because none of them are wasted.

What the curve is actually showing

The chart below the swing is a resonance curve: push rate on one axis, how wide the swing ends up settling on the other. It is built the slow way, from the simulation itself rather than a formula drawn in ahead of time — every push rate you dwell on for a moment gets tried for real, the swing is given time to settle into its steady arc at that rate, and the resulting width is logged as one point on the curve. Scrub the slider from one end of its range to the other, pausing here and there, and the shape fills itself in: small and flat out at the edges, rising steeply as the push rate closes in on 1.00, and falling away just as fast past it. That peak sitting almost exactly on 1.00 is not a coincidence built into the chart — it is the one honest fact about this system, which is that it only truly cooperates with itself at one rate.

Friction is what keeps that peak from being a single infinitely tall spike. Some energy leaks out of the system every cycle — to air, to the creak of the ropes — and at resonance the swing settles exactly where the energy coming in from your pushes equals the energy leaking out. Less friction means less leaking, so the same pushes buy a wider arc before the losses catch up, which is why dragging the friction slider down sharpens the peak and raises it, and dragging it up flattens the whole curve into a gentler hill. Look closely at a low-friction peak and you may notice it leans slightly left of 1.00 rather than sitting perfectly on it — a swing arcing wide no longer behaves quite like the simple back-and-forth it is at small angles, and a wider arc actually runs very slightly slower than a narrow one, nudging its own best rate downward as it grows. Real pendulum clocks have to be built to minimise exactly this effect.

The same curve, in places with no ropes at all

Nothing about this depends on gravity or a rope; any system with a preferred rhythm and some way of losing energy will show the same curve. A radio tuner is a tiny electrical circuit with its own natural frequency, built to be pushed by incoming radio waves — turning the dial changes that natural frequency so it lines up with one station's broadcast rate and resonates loudly with it while every other station's signal, arriving at the wrong rate, barely moves it at all. A wine glass has a natural ring; a voice holding precisely that note for long enough can, in principle, pump energy into it the same way a hand pumps a swing, crest after crest arriving exactly when the glass wall is already flexing outward. And in 1940, a mile-long suspension bridge across the Tacoma Narrows was found, within months of opening, by a wind blowing at just the wrong steady speed to match the twisting rhythm its deck preferred — it did not need a stronger wind, only a sustained one at the right rate, and the swings compounded past anything the structure could absorb.

The swing is modelled as a damped, driven pendulum — not the small-angle approximation, the real sine-of-the-angle restoring force, integrated with fourth-order Runge–Kutta — which is why its arc can genuinely bend the resonance peak rather than growing without limit. The push rate and friction sliders set the driving frequency and damping directly; a fixed push strength is applied at every rate, so nothing about how hard you are pushing ever changes — only when. ?warm= fast-forwards a scripted sweep of the slider for a representative first frame. Space gives one extra shove on top of whatever the slider is already doing.