Vibration of Masses on a String
This Demonstration shows the free vibrations of a string under tension with three equally spaced masses. You can adjust the tension, masses, and initial displacements in the system. The plots below show the displacements and velocities of the three mass centers. The system is formulated for small displacements and can be used to show the effects of tension in the line or the volume of the masses.
where is the length of the string.
The formulation can also be found in W. W. Seto, Schaum's Outline of Mechanical Vibrations, New York, McGraw-Hill, 1964.