A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional potential U ( x )= x ⁴ / 4- x ² / 2 ~J Where x is in meters. At time t =0 ~s , it is at x =-0.5 ~m . Then at a later time it c

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A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional potential U ( x )= x ⁴ / 4- x ² / 2 ~J Where x is in meters. At time t =0 ~s , it is at x =-0.5 ~m . Then at a later time it can be found

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Correct answer: C. Between x =-1.0 ~m to x =0.0 ~m

at t =0, x =0.5 aligned u &= x⁴ 4 - x² 2 1 4 1 16 - 1 4 1 2 | 1 4 | d u d x &= 4 x³ 4 - 2 x 2 =x³-x d u d x &=x (x²-1 ) aligned du dx =0 at point of maxima & minima x =0 ; x = 1 ( d ² u dx ² )_ x =0 =-1 point of maxima ( d ² u dx ² )_ x = 1 =2 point of minima particle will found between (-1,0)

A particle with total mechanical energy, which is small and negative, is under the influence of a one dimensional potential U ( x )= x ⁴ / 4- x ² / 2 ~J Where x is in meters. At time t =0 ~s , it is at x =-0.5 ~m . Then at a later time it can be found

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