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Pendulo

Simple Pendulum Physics

\[T = 2\pi\sqrt{\frac{L}{g}}\]
$21.99 USD
$21.99 USD
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Why do grandfather clocks have long pendulums? Pendulo keeps time. For small swings, a simple pendulum’s period is T = 2π√(L/g): it depends on length and gravity, not on the bob’s mass. A one-metre pendulum takes about two seconds per full swing. Galileo first noticed the timing. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

For small swings, a pendulum's period depends only on its length and gravity, not on its mass or (to a good approximation) its amplitude. Huygens used that regularity to build the first accurate pendulum clocks.

Pendulo keeps time, and only his length matters.

For small swings, a simple pendulum's period depends on its length and on gravity, and on nothing else: not the mass of the bob, and not how wide the swing is. A one-metre pendulum takes about two seconds per full swing.

LENGTH MATTERS. WEIGHT DOESN'T. A heavier bob needs more force to accelerate, and gravity supplies exactly that much more, so the two cancel, as long as air drag is negligible. Gravity does matter: the same pendulum swings slightly slower where gravity is weaker, so pendulums were used to measure it.

Galileo noticed the steady timing around 1583, reportedly by timing a swinging lamp in Pisa cathedral against his pulse. Christiaan Huygens built the first pendulum clock in 1656. The formula is the small-angle approximation: at large amplitudes the period grows a little.

Pendulo never hurries and never drags. Give him a length, and he gives you a second.

Equations

\[T = 2\pi\sqrt{\frac{L}{g}}\]
SymbolMeaningUnit
\(T\) period of one full back-and-forth swing (small swings) \(\mathrm{s}\)
\(L\) length from pivot to the centre of the bob \(\mathrm{m}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)

Sources

  1. HyperPhysics — Simple Pendulum
  2. Encyclopaedia Britannica — Pendulum

Source Huygens, C. (1673). Horologium Oscillatorium. Paris: F. Muguet.

Field notes

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