محاكي البندول
أرجِح عدة بنادول في آن واحد واكتشف ما يحدد إيقاعها حقًا: الطول والجاذبية ومقدار سحبها إلى الخلف.
هذا بندول لاخطي حقيقي، مُكامَل بطريقة RK4 — وليس اختصار الزاوية الصغيرة. اختر إعدادًا مسبقًا أو انقر على الثقل لقراءة طوله وجاذبيته وزمنه الدوري وتردده بوحدات حقيقية، وشاهد كيف يزداد الزمن الدوري الحقيقي عند التأرجحات الكبيرة.
الإعدادات المسبقة
البندول المحدد
انقر على الثقل لفحص طوله وجاذبيته وزمنه الدوري وتردده.
الصيغ والمصادر
T = 2π√(L/g)
θ″ = −(g/L)·sin θ
T = 4√(L/g)·K(sin(θ₀/2))
g₀ = 9.80665 m/s²
The units and constants behind this swing
A pendulum is a machine made of three quantities. Follow any of them into the converter, or into the constant that defines it — something a physics simulation alone cannot show you.
What you are changing
The constant in the formula
- g₀ = 9.80665 m/s² Standard gravity · a defined value, exact — not a measurement
The same 1-metre pendulum, moved around the Solar System
| Body | g (m/s²) | Period of a 1 m pendulum | vs Earth |
|---|---|---|---|
| Earth | 9.80665 * | 2.01 s | 1.00× |
| Moon | 1.62 | 4.94 s | 0.17× |
| Mars | 3.721 | 3.26 s | 0.38× |
| Venus | 8.87 | 2.11 s | 0.90× |
| Mercury | 3.7 | 3.27 s | 0.38× |
| Jupiter | 24.79 | 1.26 s | 2.53× |
| Saturn | 10.44 | 1.94 s | 1.06× |
| Sun | 274 | 0.38 s | 27.94× |
Periods are calculated live from T = 2π√(L/g) with L = 1 m. * Earth's value is the defined standard gravity g₀; the others are NASA surface-gravity figures (NIST, NASA Planetary Fact Sheet).
The pendulum that almost became the metre
A pendulum whose full swing takes exactly 2 seconds needs a length of 0.9936 m on Earth — so close to one metre that in the 17th century it was proposed as the definition of the metre itself. The definition went to the speed of light instead, but the coincidence is still there in the numbers above.
How the units are actually defined →