Home / Topics / Oscillations & SHM
Simple pendulum in elevator
Intermediate
Effective gravity changes with acceleration of the support.
In an elevator accelerating up with a, the effective gravity is g + a; so T = 2π√(L/(g + a)). In free fall the pendulum doesn't swing.
a = 2 m/s²: T is 9% shorter.
Use g_eff.
In more detail
In an accelerating elevator, the effective value of g changes, and so does the pendulum period. Accelerating upward increases the effective g and shortens the period.
Real-world uses
- Physics problems use this to test understanding of effective gravity.
- Accelerometers can be calibrated using pendulum periods in different frames.
- A pendulum in an accelerating lift swings with a different period, because the effective gravity changes with the acceleration.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What happens in free fall?
The effective g is zero, so the pendulum does not oscillate about its equilibrium.
Does the period increase or decrease going up?
It decreases, because the effective gravity increases.
What effective gravity does the pendulum feel in a lift accelerating upward?
The effective gravity is g plus the lift's acceleration, which shortens the period.
Related topics in Oscillations & SHM
Physical pendulum · Torsional pendulum · Second's pendulum · Energy in SHM · Kinetic and potential energy in SHM · Average energy over a cycle