Pendulum 주기 공식 (T = 2π√(L/g)): 계산기 & 예제

계산 방법 pendulum 주기 with T = 2π√(L/g). 풀기 for length or g, with 일ed examples and a free pendulum 주기 calculator.

계산 방법 Pendulum 주기 (Quick 답)

For a small-angle simple pendulum, the 주기 is T = 2π √(L/g). That is the 공식 people write as T = 2π√(L/g) or t = 2π√(l/g). Multiply 2π by the square root of length over g. The answer is in seconds.

  • Measure L from the pivot to the c입력 of the bob (meters).
  • Use the paper’s g (often 9.8 or 9.81 m/s²).
  • 계산 T = 2π √(L/g). 주파수 is f = 1/T.
  • To find length: L = g T² / (4π²). To find g: g = 4π² L / T².

    • Need a 확인ed number now? Open the free pendulum 주기 calculator (T = 2π√(L/g)) — then come back for lab traps and 일ed examples.

    What Is T = 2π√(L/g)?

    A simple pendulum is a small bob on a light inextensible string. In the intro-physics small-angle model (about 15° or less from vertical), the motion is simple harmonic. 주기 depends on length and gravity — not on 질량, and not on how far you pull the bob.

    L is pivot-to-c입력 length. Doubling L multiplies T by √2, not by 2. Large angles need a more advanced 공식; home일 usually wants the small-angle form.

    Rearrangements

  • T = 2π √(L/g) — 주기 in seconds.
  • f = 1/T — 주파수 in hertz.
  • L = g T² / (4π²) — length in meters.
  • g = 4π² L / T² — local gravity from a lab timing.

    • 풀기 any of these on the free pendulum calculator.

    Where the 공식 Comes From

    For small θ in radians, sinθ ≈ θ. The tangential restoring 힘 is −mg sinθ ≈ −mg (s/L). Then a = −(g/L) s, which is SHM with ω² = g/L, so T = 2π/ω = 2π √(L/g).

    Same SHM idea as a 질량 on a spring — 비교 with the simple harmonic motion calculator.

    단위

  • Length L → meters (80 cm = 0.80 m).
  • g → m/s² (9.8 or 9.81 unless the paper says otherwise).
  • T → seconds. f → Hz.

    • 풀이 예제

    예제 1: T for a 1.0 m pendulum

    L = 1.0 m, g = 9.8 m/s². T = 2π √(1/9.8) ≈ 2.007 s. f ≈ 0.498 Hz.

    예제 2: length for T = 2.0 s

    L = g T² / (4π²) = 9.8 × 4 / (4π²) = 9.8/π² ≈ 0.993 m. A “2-second pendulum” is just under one meter on Earth.

    예제 3: estimate g in the lab

    시간 50 swings totaling 100.35 s → T = 2.007 s, with L = 1.00 m. g = 4π² L / T² ≈ 9.80 m/s². 시간 many cycles; divide total time by the count.

    확인 예제 1–3 on the pendulum calculator.

    흔한 실수

  • Leaving L in centimeters while g is in m/s².
  • Assuming T doubles when L doubles (T scales with √L).
  • Using the small-angle 공식 for a very wide swing without saying so.
  • Measuring string length only and skipping the radius of a large bob.
  • Thinking 질량 changes the 주기 in the ideal model — it does not.

    • 무료 Pendulum 주기 계산기

    Use the free pendulum 주기 calculator to solve T = 2π√(L/g) for 주기, length, or g with 단계별 일ing.

    SHM calculator.

    Hooke's law calculator — spring SHM uses T = 2π√(m/k).

    위치 에너지 (PE = mgh) — related gravity home일.

    Master T = 2π√(L/g) with L in meters — then verify every home일 answer on the calculator.

    문서

    • 탄성 위치 에너지 공식 (U = ½kx²): 계산기 & 예제
    • 계산 방법 전기 전력 (P = VI, I²R, V²/R)
    • 계산 방법 파동 속도 (v = fλ): 주파수 × 파장
    • 계산 방법 무게 (W = mg): 질량 vs 힘
    • 계산 방법 밀도 (ρ = m/V): 질량 ÷ Volume
    • 계산 방법 가속도 (a = (v − u)/t)

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