F=ma 2025 Problem 18

Physics · mechanics

Problem

Question: A particle of mass

m

moves in the

{xy}

plane with potential energy

U(x,y) = {kxy}/2

. If the particle begins at the origin, then it is possible to displace it slightly in some direction, so that the particle subsequently oscillates periodically. What is the period of this motion? (A)

2\pi\sqrt{m/{4k}}

. (B)

2\pi\sqrt{m/{2k}}

. (C)

2\pi\sqrt{m/k}

. (D)

2\pi\sqrt{{2m}/k}

. (E)

2\pi\sqrt{{4m}/k}

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