# q03 - Physics 3221 Mechanics I Fall Term 2010 Quiz 3 This...

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Unformatted text preview: Physics 3221 Mechanics I Fall Term 2010 Quiz 3 This is a 10 min. quiz (closed book). There are two multiple choice problems. Problem 1. [2.5 pts] A particle of mass m moves in a one-dimensional potential V ( x ) = ax 2- bx 4 , where a and b are positive constants. The angular frequency w of small oscillations about the minimum of the potential is equal to (A) radicalBig 4 b m (B) radicalBig a 2 b (C) 2 π radicalBig a m (D) 2 π radicalBig m a (E) radicalBig 2 a m Solution. E. The potential has three extrema, but only the one at x = 0 is a minimum. Then the equation of motion is m ¨ x = F x =- dU dx =- 2 ax + 4 bx 3 ≈ - 2 ax ¨ x + 2 a m x = 0 from where ω 2 = 2 a m . Notice that answers A, B and D can be ruled out simply on dimensional grounds (they have the wrong units). Problem 2. [2.5 pts.] A particle of mass m undergoes harmonic oscillation with period T . A retarding force f proportional to the speed v of the particle, f =- bv is introduced. If the particle continues to oscillate, the period with...
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q03 - Physics 3221 Mechanics I Fall Term 2010 Quiz 3 This...

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