By Y. Choquet-Bauhat, et al.,
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Additional info for Analysis, Manifolds and Physics [Part 2]
L under a given force is promass. l/1 0 is called the strain. This result can also be expressed by saying that in a static experiment with a given rod, the displacements of various points along it are proportional to their distances from the fixed end, as shown in Fig. P along the whole length of the rod. 2. l/1 0 ) is caused by applying forces proportional to the cross-sectional areas, as in Fig. 3-4(b). P /A is called the stress and has the dimensions of force per unit area, or pressure. 3. 13 of the normal length l 0 , the relation between stress and strain is linear, in accordance with Hooke's law.
V2), there would exist no time, however long, after which the preceding pattern of displacement would be repeated. 24 The superposition of periodic motions t=O I I I 400/sec 600/sec (a) 400/sec 600/sec (b) I I 1 t=O Fig. 2-5 (a) Superposition of two commensurable sinusoids, offrequencies 400 sec- 1 and600 sec- 1 , whose maxima coincide at t = 0. (b) Superposition of same sinusoids if their zeros coincide at t = 0. ) combining frequencies, but with an amplitude that varies periodically with time-one cycle of this variation including many cycles of the basic vibration.
3-1) or (3-2), even if the system itself is not a single object on an effectively massless spring. In Eq. (3-3) it is to be noted that the constant w is defined for all circumstances by the given values of m and k. The equation contains two other constants-the amplitude A and the initial phase a-which between them provide a complete specification of the state of motion of the system at t = 0 (or other designated time) in any particular case. The initial statement of Newton's law in Eq. (3-1) contains no adjustable constants.
Analysis, Manifolds and Physics [Part 2] by Y. Choquet-Bauhat, et al.,