On Periodic Solutions of an Atwood's Pendulum.

An Atwoods pendulum is defined as an Atwoods machine in which one of two masses is allowed to swing as a pendulum while the other remains constrained to move only in the vertical direction. The pendulum motion of the one mass induces a varying tension in the connecting wire this, in turn, produces motion in the second mass. It is shown that this motion can be made periodic if the ratio of the two masses and the dependency of this ratio on the initial conditions are chosen as prescribed in this report. Is this condition is not met, the motion consists of the superposition of two motions. The first is notiion in a constant gravitational field where the effective gravity is kg the factor k is determined explicitly. The second is the periodic motion that is the central theme of this report. During the course of the analysis, the fundamental frequency of the periodic motion is determined. It is shown to be slightly higher than the frequency of a pendulum of comparable length swinging in the earths gravitational field the factor is given explicitly. This work is restricted to the extent that small approximations are introduced initially for trigonometric functions