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# Periodic motion in a playground swing

Children sometimes talk about twin swinging, where two children swing together, next to each other, moving back and forth in sync. Similarly, sibling swinging describes two swings moving in opposite directions, completely out of phase.

The figure to the right shows two preschool teachers ready to investigate if it is possible to twin swing with an empty swing. If they let go at the same time, they will be in phase as they start. The angle is approximately the same, corresponding to both swings having approximately the same amplitude at the start. If they return together, the also have the same period. Typically twin swinging can work with two similar swings and often also with an empty swing, although you may need to lower the center of mass by lying down on the swing.

The concepts relating to periodic motion are thus relevant already for children in playground swing.

## Mass independence and the equivalence principle

It is worth noting that the period is independent of the pendulum mass. This follows from the equivalence between inertial mass (as in ma) and gravitational mass (as in mg):

This can be investigated in the classroom with a set of small objects suspended on a timeline at a position corresponding to the period (or half-period) of each pendulum. This can also be used to obtain a graph of the relation between period and pendulum length. Remember that a 1 meter long pendulum has half-period close to 1 second. (Think about grandfather clocks!)

Note how the Danish 1, 2, and 5 DKK coins with different masses follow the same curve and also the same curve as the cuddly animals on strings!