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A particle of mass \( m \) free to move in the \( x-y \) plane is subjected to a force whose components are \( F_{x}=-k x \) and \( F_{y}=-k y \), where \( k \) is a constant. The particle is released when \( t=0 \) at the point \( (2,3) \). Prove that the subsequent motion is simple harmonic along the straight line \( 2 y-3 x=0 \).
\( \mathrm{P} \)
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