Physical Pendulum Calculator

Your details

Total mass of the rigid body. Metric: kilograms; imperial: pounds.
kg
Rotational inertia of the body about the pivot axis. Use the parallel-axis theorem: I_pivot = I_cm + m*d^2.
kg-m2
Distance from the pivot point to the centre of mass of the body along the pendulum axis.
m
Starting angular displacement from vertical. Below 15 degrees the small-angle approximation is accurate to within 0.5%. Above 30 degrees the period increases noticeably.
deg
Standard Earth gravity is 9.81 m/s^2. Change this to model other planets: Moon 1.62, Mars 3.72, Jupiter 24.79.
m/s2
PeriodNormal oscillation
1.5859s

Time for one complete oscillation (small-angle approximation)

Frequency0.6305Hz
Angular frequency3.9618rad/s
Equivalent simple-pendulum length0.625m
Maximum potential energy0.2674J
Max angular velocity1.0342rad/s
Max linear velocity at CM0.4137m/s
Small-angle approximationGood (error < 5%)
1.5859 s
Very fast<0.5Normal0.5-2Slow2-5Very slow5+

Period 1.5859 s, angular frequency 3.962 rad/s

  • The period is 1.5859 s, meaning the pendulum completes 0.631 full oscillations every second.
  • This physical pendulum behaves identically to a simple pendulum 0.625 m long. You can use that length to cross-check or simplify related calculations.
  • Starting from 15 degrees, the system stores 0.2674 J of potential energy. At the lowest point the centre of mass reaches 0.414 m/s.

Next stepThe small-angle approximation is reliable at 15 degrees. To lengthen the period, increase the moment of inertia or move the pivot closer to the centre of mass.

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