Solutions_HW7 - Rachel 4o l

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Rachel Lee Physics 601 Homework 7---Due Friday October 29 4o l<o You may find Mathematica very helpful for some of these problems!! 1, Three beads are free to move along a wire. They are connected two immovable walls by 4 springs. The masses and spring constants are as indicated on the figure. . a. Find the normal modes and their associated frequencies by finding the eigenvectors and eigenvalues of the appropriate matrix. . b. Verifu that the modes are orthogonal witi respect to the mass matrix. "c. Suppose at t=0 all three particles are in their equilibrium positions with the two particle on the end at rest and the one in the middle moving with velocity v. [This can happens as a result of an impulse acting on the middle particleJ. Find the motion ofthe three particles. ' 2. Consider the system described in the previous problem. Suppose that all the particles begin at rest in equilibrium a force given by/(r) = f sinh(r/7")0(l) acts on the middle particle. Use Green's functions to determine the motion of the three particles. . 3. Co4q4!e13n infinite ch4in qf q4qsqe_q and springs as shown below: 2mm2mm2mm 2m
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A I LIMITED-LIABILIry COMPANIES (LLCs) It may take some searching, but there's a lid for every pot. -ANONYMOUS Mary L--was a schoolteacher who lived with her husband and four children near Seattle, Washington. In the early 1990s, Mary purchased a gray Volkswagen Fox. In all innocence, she titled the car in her own name. Not in her wildest dreams-or night- mares!-could Mary have foreseen the bitter consequences of driving a car with plates that would show up in the computer with her first name, middle initial, and last name. Years passed. Unexpectedly, Mary fell in love with one of her students, a thirteen-year-old boy. Despite being married, she was unable to control her emotions. One thing led to another and Mary found herself pregnant. In 1977 , the affair became known. She was arrested, jailed, and sentenced to eighty-nine months in prison. Given her lack of a criminal record and the fact she posed no threat to society, Mary was released on parole. One of the
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The masses alternate between two types, one twice as heavy as the other. The springs connecting the masses are all equal and in equilibrium the masses are all a distance a apart. The masses are constrained to move longitudinally. Find the dispersion relation relating frequency to wave number. Three beads are free to move along a wire. They are connected two immovable walls by 4 springs. The masses and spring constants are as indicated on the figure. The third particle.ia**end has a mass q. The first particle- is attached to a shock absorber with a force given by F : -maoi where arj : a. Using the . la\ - (o (i)-' \ phase-space formalism derived in class: ri = | '-l W :l -- .: '- , I with the ' \n) \-Y -F(n-'l Suppose the system described in the problem above has the middle particle charged fwith charge qJ and is place in an electric field, oriented to the right with a magnitude of E = E,tcos(2a.t)
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This note was uploaded on 12/29/2011 for the course PHYSICS 601 taught by Professor Hassam during the Fall '11 term at Maryland.

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Solutions_HW7 - Rachel 4o l

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