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⋅$$A4$$ $$K(x)=Umax$$−$$U(x)=$$β$$A4$$−β$$x4=$$β$$A4$$−$$x4$$    $$U(x)=13K(x)$$   (Given)∴     β$$x4=13$$β$$A4$$−$$x4$$⇒    $$x=$$±$$A2$$

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)= $β$ 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

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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

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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)= $β$ 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