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Unformatted text preview: Ph507. Homework 2 (due: Friday, February 4).PROBLEM 21 (3 pts)Considetr a relativistic particle in an external potential,U=kx:L=−mc2r1−˙x2c2−kxFind the period of its oscillations as a function of amplitudex.PROBLEM 22 (2 pts)A "waterslide" has a shape given by the following 3D curve:x(z) =zcos (2πz/λ),y(z) =zsin (2πz/λ)Herethe positive direction ofzis taken to be downward, parameterλis unknown, and this spiral path makesNtotalturns (assumeNÀ1). Find the overall travel time down this slide, if the initial andfnal speeds are zero andv,respectively. Neglect dissipation.PROBLEM 23 (7 pts)A particle of massmis confned by potentialU(x). Find the period of its oscillations, as a function of the totalenergyE.(a)U(x) =Utan2(x/ξ);(b)U(x) =U£e−2x/ξ−2e−x/ξ¤;(c)U(x) =−Uh(x/ξ)2−1i2. Express the result in terms of elliptic integralK(z).PROBLEM 24 (3 pts)Due to the presence of ions, electrostatic interactions are normally "screened" in water. For example, electrostaticDue to the presence of ions, electrostatic interactions are normally "screened" in water....
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 Spring '04
 ANON
 mechanics, Work, Hyperbolic function, exp exp, overall travel time, following PoissonBoltzmann equation, e.g. biological membrane

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