# Frictionless swing

Integral
Staff Emeritus
Gold Member
From simple energy considerations, it is not clear that friction has anything to do with the motion resulting from a change in CM (Center of Mass). As a pendulum swings the bob is continually changing in height, this is reflected in a change in Potential energy, this of course results in a change in kinetic energy.

When a rider pumps a swing, s/he is mimicing this change in potential energy by raising and lowring the CM of the swing system. The change in PE MUST be reflected in a change in KE. Thus the simple act of rocking back and forth is sufficient to set a swing into motion. As long as the frequency of the CM change is harmonic with the natural frequency of the swing motion will occur. The only need for friction is to keep your hands and bottom on the swing.

When standing you raise the CM considerably, thus reducing the natural frequency, further, when standing your mass is not concentrated, thus you need to do the analysis as a physical pendulumn with a distributed mass. Things change.

Integral,
When a rider pumps a swing, s/he is mimicing this change in potential energy by raising and lowring the CM of the swing system. The change in PE MUST be reflected in a change in KE. Thus the simple act of rocking back and forth is sufficient to set a swing into motion. As long as the frequency of the CM change is harmonic with the natural frequency of the swing motion will occur.
However, can the (frictionless) swing remain in harmonic motion once the bob's rocking (started from a dead hang) has stopped?

Integral
Staff Emeritus
Gold Member
Originally posted by Loren Booda
Integral, However, can the (frictionless) swing remain in harmonic motion once the bob's rocking (started from a dead hang) has stopped?
Looks to me like once the motion begins, it is simply a pendulumn. If no further pumping occurs, and there is no friction at the piviot, motion will continue indefinatly. The conversion between kinetic and potential energy will continue without loss.

Njorl