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problems_HW6

# problems_HW6 - Homework 6 Classical Mechanics(Phys701 Due...

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Homework 6 Classical Mechanics (Phys701) Due: November 28, 2011 Problem 6-5 (a) In the linear triatomic molecule, suppose the initial conditions is that the center atom is at rest, but displaced by an amount a 0 from equilibrium, the other two being at their equilibrium points. Find the amplitudes of the longitudinal small oscillations about the center of mass. Give the amplitudes of the normal modes (b) Repeat part (a) but with the center atom initially at its equilibrium position but with initial speed v 0 . Problem 6-6A A five-atom linear molecule is simulated by a configuration of masses and ideal springs that looks like the following diagram (see the book). All force constants are equal. Find the eigenfrequencies and normal modes for longitudinal vibrations. Hint: transform the coordinates η i to ζ i defined by η 3 = ζ 3 , η 1 = ζ 1 + ζ 5 2 , η 5 = ζ 1 - ζ 5 2 with symmetrical expressions for η 2 and η 4 . The secular determinant will then factor into deter- minants of lower rank.

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