A particle of mass \( m \) is executing oscillations in straight line about its mean position wi...

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A particle of mass \( m \) is executing oscillations in straight line about its mean position with amplitude \( A \). The potential energy of the particle is given as \( \mathrm{U}=-a \mathrm{x}^{4} \), where \( a \) is a positive constant and \( x \) is the displacement of the particle form its mean position. Find the displacement of the particle from its mean position where its potential energy is one third of its kinetic energy.
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