| Title: | Center of oscillation |
| Original Title: | Centre d'oscillation |
| Volume and Page: | Vol. 2 (1752), p. 826 |
| Author: | Jean-Baptiste le Rond d'Alembert (biography) |
| Translator: | Charles Ferguson [Colby College, Emeritus] |
| Original Version (ARTFL): | Link |
| Rights/Permissions: |
This text is protected by copyright and may be linked to without seeking permission. Please see http://quod.lib.umich.edu/d/did/terms.html for information on reproduction. |
| URL: | http://hdl.handle.net/2027/spo.did2222.0003.071 |
| Citation (MLA): | d'Alembert, Jean-Baptiste le Rond. "Center of oscillation." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Charles Ferguson. Ann Arbor: Michigan Publishing, University of Michigan Library, 2017. Web. [fill in today's date in the form 18 Apr. 2009 and remove square brackets]. <http://hdl.handle.net/2027/spo.did2222.0003.071>. Trans. of "Centre d'oscillation," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 2. Paris, 1752. |
| Citation (Chicago): | d'Alembert, Jean-Baptiste le Rond. "Center of oscillation." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Charles Ferguson. Ann Arbor: Michigan Publishing, University of Michigan Library, 2017. http://hdl.handle.net/2027/spo.did2222.0003.071 (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Centre d'oscillation," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 2:826 (Paris, 1752). |
Center of oscillation, the point on the suspension line of a compound pendulum where, if the entire mass of the pendulum were concentrated there, the oscillations would have the same duration as previously. See Oscillation.
The distance from the suspension point is therefore equal to the length of a simple pendulum whose oscillations are isochronous with those of the compound pendulum. See Pendulum and Isochronous.
Laws of the center of oscillation . If several weights, B H F and D ("Mechanics" plate II, Figure 22), whose mass is assumed to be concentrated at points D F H and B, remain at the same distance from each other and from suspension point A, and if this compound pendulum oscillates around point A, the distance OA from the center of oscillation O to the suspension point will be found by multiplying the various weights by the square of the distances, and dividing the total by the sum of the momentums of the weights.
To determine the center of oscillation on a straight line AB (Figure 23), let AB = a and AD = x; the infinitely small particle DP will equal dx, and the momentum of its weight xdx, consequently the distance from the center of oscillation on part AD to the suspension point A will be
now let a be substituted for x, and the distance from the center of oscillation on the total line AB will be 2/3 a; this is how the center of oscillation is found for a length of wire oscillating from one of its ends.
For the center of oscillation of an equilateral triangle CAB (Figure 18) oscillating on an axis parallel to its base CB, the distance from vertex A is 3/4 of the height of the triangle, AD.
For an equilateral triangle CAB (Figure 18) oscillating on its base CB, the distance from vertex A is 1/2 of AD, the height of the triangle.
In the Mémoires de l'Académie des Sciences , 1735, M. de Mairan comments that several authors have erred in their formulas for centers of oscillation , among them M. [Louis] Carré, in his [1700] book on integral calculus.