Pendulum Lab

H2 Physics · Oscillations — exact θ″ = −(g/L)·sin θ vs the SHM approximation

θ(t) — exact vs small-angle prediction

θ(t) exact (RK4) θ₀·cos(ωt) SHM approx

Try first: drag θ₀ to 60° — watch the two periods split.

Length L1.00 m

Release angle θ₀30°

SHM holds below ~10°; splits by 60°.

Bob mass m1.00 kg

m is not in T = 2π√(L/g) — period won't budge.

Gravity g9.81 m/s²

Home turf: T is the familiar 2π√(L/9.81).

ⓘ more

T measured averages successive same-direction zero crossings of θ from the RK4 integration — a stopwatch on the real motion, not the formula.

What to notice

›T = 2π√(L/g) — mass is absent. Change m mid-swing; nothing happens to the period.
›The formula assumes sin θ ≈ θ, so it only holds for small angles. At θ₀ = 5° measured and predicted agree; at 60° the real period runs ~7% long.
›On the Moon g drops 9.81 → 1.62 m/s², so T grows by √(9.81/1.62) ≈ 2.46×. Same pendulum, slower clock.