Question

Is is possible to set a swing into oscillations without touching the ground? This occurred to me while watching the second pirates movie. There is a scene where the ship's crew is suspended in a cage from a bridge in between two cliffs. They escape by swinging the cage towards one of the cliff. Is that even possible?

Update: From the answers, it is clear that it is possible to make the swing oscillate. Assuming the model Mark has proposed would there be limits to much you can swing? Is it possible to quantify it?

Answer 1

Yes, you can start swinging.

Imagine a swing in a two-dimensional world. The swing consists of a stiff rod hanging down from a ceiling rigidly attached to a bowl with a ball inside. The rod can swing freely about its connection point to the ceiling, so it's a pendulum. The bowl is a section of a circle whose radius of curvature equals the length of the rod. The ball slides frictionlessly inside the bowl, except that it can exert a force on the bowl at any time if it wants to.

The reason for choosing this system is that as the bowl swings, the physical space it occupies doesn't change much. A swinging motion is as if a little bit of the bowl gets lopped off one side and pasted on to the other. This means that from the ball's point of view, as long as all oscillations remain small, the bowl is essentially stationary, and the ball oscillates like a pendulum.

The bowl itself also oscillates like a pendulum, but it does so at a different frequency. If you write down the equations of motion for the system, you find that the ball oscillates with angular frequency , but the bowl oscillates with angular frequency , with half the angular size of the bowl.

Suppose we start from the equilibrium position with the bowl and ball at rest at the bottom of the swing. If the ball momentarily exerts a force on the bowl, they will begin oscillating in different directions. Because they have different frequencies, they will eventually both be displaced in the same direction. When that happens, have the ball latch on to the bowl and cease all motion relative to the bowl. At this point you have a swing that's displaced from equilibrium - you're swinging.