A particle of mass m is executing oscillations about the origin on the $$X-axis$$ with amplitude A. Its potential energy is given as $$U(x)$$ $$=$$ β$$x4$$ where β is a positive constant. The $$x-coordinate$$ of the particle, where the potential energy is $$one-third$$ of the kinetic energy, is

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 $$U(x)$$ $$=$$ β$$x4$$ where β is a positive constant. The $$x-coordinate$$ of the particle, where the potential energy is $$one-third$$ of the kinetic energy, is

Infinity Learn · Accepted Answer

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

A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy is given as $U (x) = {βx}^{4}$ 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 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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy is given as $U (x) = {βx}^{4}$ where $β$ is a positive constant. The x-coordinate of the particle, where the potential energy is one-third of the kinetic energy, is