# set3 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University Third Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 31 no class, Jun 9 9:30am-11:18am Fnal exam Due date: Thursday, Apr 15 7. Anharmonic oscillator 8 points As another example of an anharmonic oscillator, we will consider a particle of mass m that moves in one dimension under the in±uence of the force F ( x ) = - F 0 x | x | = + F 0 x < 0 0 x = 0 - F 0 x > 0 a) Calculate the potential U ( x ) corresponding to this force with U ( x = 0) = 0. [Hint: calculate the potential independently for x > 0 and x < 0 and piece your solutions together afterward.] b) Derive the relation ˙ x ( x ) and draw the phase portrait for this anharmonic oscillator. c) Solve the equation of motion of the anharmonic oscillator for the initial conditions x (0) = A and ˙ x (0) = 0 for times t during which x ( t ) > 0. d) Calculate the dependence of the period

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set3 - Department of Physics The Ohio State University Prof...

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