A particle moves along the x -axis with potential energy U ( x ) = k [ 1 − exp ( − x 2 )] for − ∞ ≤ x ≤ + ∞ , where k is a constant of appropriate dimensions. Then:

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PhysicsSHMOscillations and SHMMedium2 min

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A particle moves along the $x$ -axis with potential energy $U (x) = k [1 - exp (- x^{2})]$ for $- \infty \leq x \leq + \infty$ , where $k$ is a constant of appropriate dimensions. Then:

Options:

Answer:

Solution:

Near $x = 0$ , $U \approx k x^{2}$ , a parabola: SHM. The force $- d U / d x = - 2 k x e^{- x^{2}}$ points toward the origin, so (A) and (B) are wrong. With $E = k /2$ the KE is maximum (not minimum) at the origin where $U = 0$ .

Subject:PhysicsTopic:SHMSubtopic:Oscillations and SHM

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