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3-14a)] while for ˜2 <^ 1, M(t) a n d J(t) are reciprocals (Problem 2-2). 4. T h e most i m p o r t a n t result of this chapter is that a n y o n e response function m a y b e used t o characterize t h e anelastic behavior of t h e m a terial, since all other response functions m a y b e derived from it with t h e 40 2 TH E BOLTZMAN N SUPERPOSITIO N PRINCIPL E aid of t h e Boltzmann principle. Although this is a major step forward, it does n o t meet all t h e r e q u i r e m e n t s of a complete formal theory.

1-4. W o r k out the form of the constants CX and C 2 in E q s . 5-1) for the case of the torsion p e n d u l u m in t e r m s of the m o m e n t of inertia GENERAL REFERENCES 29 / of the inertia m e m b e r , as well as the length / and the radius a of the specimen wire. Also, show that the proportionality constant in E q . 5-11) is na^lll 1-5. Verify E q s . 5-8). 1-6. Show that the quantity ¢ defined by E q . 5-10) is t h e magnification factor of the resonant system, in the sense that the amplitude excited at resonance is ¢ times the deflection that the same peak force would produce if applied statically.

W h a t was not considered, however, was the response to different stresses (or strains) imposed at different times. W e will see in the present chapter that only the full consequences of linearity, as embodied in the Boltzmann principle, p e r m i t us to d e d u c e all of the relationships between the response functions. Consider that a stress is applied at time t{. 1-1) N o w , suppose that a whole series of a t (i = 1, 2, . . , m) are applied, at successively increasing times £/, t2’, . , t m\ respectively.