In 1929, Rinkel proposed a different method to calculate  while using the Rüchardt apparatus: he noted that it may be shown that the vertical distance L which the sphere falls before it begin to rise is: , so  may be calculated from measured values of L, m, V, P and A.
In 1951, Koehler and later, in 1972 Flammersfeld introduced a trick in the original Rüchardt setup, to increase the number of oscillations that are limited by the unavoidable friction-damping and gas leak (through the piston-tube seal): they made a thin hole on the tube (at half-height) and provided a gas-feeding pump to keep the pressure inside the vessel constant. By properly trimming the gas inlet flux (through a throttling valve) they obtained the following result: during the oscillations the piston is pushed-up by the gas overpressure until it crosses the hole position; then the gas leakage through the hole reduces the pressure, and the piston falls back. The force acting onto the piston varies at a rate that is regulated by the piston oscillation frequency leading to forced oscillation; fine adjustment of the throttle valve allows to achieve maximum amplitude at resonance.
In 1958, Christy and Rieser used only a gas-feeding pump to stabilize the gas pressure.
A slightly different solution was found in 1964 by Hafner who used a tapered tube (conical: slightly larger at the top).
In 1959, Taylor used a column of mercury oscillating inside a U-shaped tube instead of the Rüchardt sphere.
In 1964, Donnally and Jensen used a variable load attached to the Rüchardt sphere in order to allows frequency measurements with different oscillating mass.
In 1967, Lerner suggested a modified version of the Taylor method (with mercury replaced by water).
In 1979, Smith reported a simplified version of the complex Rüchardt-resonance method, originally invented by Clark and Katz, in which an oscillating magnetic piston is driven into resonance by an external coil.
In 1988, Connolly suggested the use of a photogate to measure more precisely the frequency of the Rüchardt sphere.
In 2001, Severn and Steffensen used a pressure transducer to monitor the pressure oscillations in the original Rüchardt setup.
In 2001, Torzo, Delfitto, Pecori and Scatturin implemented the version of Rüchardt apparatus (shown in the top picture) using three sensors: a sonar that monitors the breast-pump oscillations, and pressure and temperature sensors that monitor the changes in pressure and temperature inside the glass vessel.