My bird, Tucker, has a swing in his cage, and the way it is hung up makes it act like a pendulum. The length of the swing is 15 cm, or .15 m, and since it is obviously on Earth, the acceleration due to gravity is 9.8 m/s^2. This allows me to use the equation for period of a pendulum. This gave me an answer of .777 seconds.
The only issue with this is that there is friction between the cage and the swing. This causes the swing to slow down and come to a stop eventually.