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Unformatted text preview: he zero of potential energy at X = 0, then ':lax2 + ~bX4. (b) A graph of U(x) for X ~ 0, .:,..... . 3 =5 N/m, b = 2 N/m and x is in meters, is <(Note that the potential energy is symmetric, '==:)J(x), but that only positive displacements idered in this problem.) The conservation. of an be written in terms of the total energy, (dx/dt)2 + U(x), so that dx/dt = ..,.U(x)J/m. The maximum speed occurs when anlinimumj i.e., dU/dx = 0, and d2Ufdx2 > o. the derivative, one finds 0 = ax + bx3, which tionsx = 0 and x = :f:VO]b = :f:.j512 m = The second derivative d2U jdx2 = a + 3bx2 IVEdorx = 0, which is a local maximum, but is .~f(}r = i:..,JO:Jb, which are minima with )U(:f:VOJb) = a2/4b = (25/8) J = 3.13 J. i~teal physical motion (K ~O) for total energy iii; The turning points (where dx/dt = 0) can from the equation U(x) = Ej there are four positive) for energies with Umin < E < solutions (one positive) for E > O. ~~!~;JIJ;~5
~ ..L+ ..J.
; x(m) =~":::": :r:J~.{~):.'C.t ...
5 : 6 t.. L.tl
. j 3 FIGURE .. . 836 Problem 44. x Solution
The f...
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 Spring '08
 WORMER
 Physics, Conservation Of Energy, Energy, Work

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