Pendulum Lab

Class XI · Oscillations / SHM: compare small-angle theory with the real ODE.

θ vs. t (last 8 s)

window: 0.0–0.0 s

Controls

Length L1.000 m

Gravity g9.80 m/s²

Initial angle θ₀20 °

Damping ξ0.000

Live readouts

T (small angle)2.007 s

T (measured)…

Error vs. theory…

ω = √(g/L)3.13 rad/s

Formula

Small angle (θ « 1):
  θ(t) = θ₀ cos(ω t),  ω = √(g/L)
  T  = 2π √(L/g)

Full ODE:
  θ̈ = −(g/L) sin θ − ξ θ̇

Try this: Set θ₀ = 5°: measured T matches 2π√(L/g) almost exactly. Now push θ₀ to 60°. The real period grows : the small-angle formula under-predicts T. That’s why JEE problems say “small oscillations”.

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