Set the length, initial angle and gravity to get the period T = 2π√(L/g), frequency and a live swinging animation with energy exchange.
Pendulum
Live readings
Angle θ0.0°
Height h0.000 m
Velocity v0.00 m/s
Kinetic energy0.00 J
Potential energy0.00 J
Total energy0.00 J
Kinetic energyPotential energy
Kinetic energyPotential energy
1.00 m
30°
9.81
Presets
1.00 kg
Mass does not affect the period — only the energy values.
1.0×
2.006 s
Period T
Small-angle approximation
0.498 Hz
Frequency f
ω = 3.132 rad/s
2.022 s
Exact period
Accounts for large amplitude
T = 2π·√(L / g)
The formula T = 2π√(L/g) is exact only for small angles (θ ≲ 20°). For larger amplitudes the real period grows; the Exact period value uses the full amplitude correction.
Drag the Length, Angle and Gravity sliders to set up the pendulum. Press Play to release it — the bob swings following the true equation of motion, and the readings show the angle, height, velocity and the kinetic / potential energy exchange in real time. Use the Speed slider to slow down or speed up the animation; Reset returns the bob to its initial angle.