Potential energy of a particle is U(x) = 2x³ - 9x² + 12x, where U is in joule and x is in metre. If the motion is SHM, find the potential energy at the mean position.
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Potential energy of a particle is U(x) = 2x³ − 9x² + 12x, where U is in joule and x is in metre. If the motion is SHM, find the potential energy at the mean position.

G1 Physics · Accepted Answer

U(x)=2x³−9x²+12x. Equilibrium points satisfy dU/dx=6x²−18x+12=6(x−1)(x−2)=0. Stability requires d²U/dx²>0; at x=2 it is positive. Therefore the mean position is x=2 m and U(2)=16−36+24=4 J. Correct answer: B.