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Q.

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) = βx4 where β is a positive constant. The x-coordinate of the particle, where the potential energy is one-third of the kinetic energy, is

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a

±A2

b

±A2

c

±A3

d

±A3

answer is .

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Detailed Solution

U = βx4(Given)∴ Umax = β.A4k(x) = Umax-U(x) = β.A4-β X4=β(A4-x4)U(x) = 13K(k) (Given)∴ βx4 = 13β(A4-x4)⇒3βx4 = βA4-βx4 4βx4 = βA4 ⇒ x4 = A44⇒x = ±A2

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