A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. Its potential energy is given as U x = α x 4 , where α is a positive constant. The x-coordinate of mass

Question

A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. Its potential energy is given as U x = α x 4 , where α is a positive constant. The x-coordinate of mass where potential energy is one-third the kinetic energy of the particle is

TestHub · Accepted Answer

The energy of oscillation is E = α A 4 ∴ the kinetic energy of mass at x = x is K = E - U = α A 4 - x 4 Given, K = 3U ∴ α A 4 - x 4 = 3 α x 4 Or x = ± A 2

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