Restoring Force for a Slinky's Fundamental Oscillation

Philip Gash

California State University, Chico

A Slinky s fundamental oscillation is the lowest order standing longitudinal wave the Slinky supports. Its frequency is determined by solving a transcendental equation obtained from a wave equation solution. To evaluate the frequency a so-called "Slinky effective mass" is employed in spite of the fact a Slinky has a well dened mass. The solution s mathe- matical complexity obscures a signicant Slinky property which simplies determination of the oscillation frequency: The restoring force acting upon the Slinky s center of mass is produced by only the coils between it and the support. Experimental evidence is presented to verify the aforementioned property. PACS numbers: 01,02,45 Keywords: mechanics, oscillations,springs, center of mass