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Two blocks of masses \( m_{1} \) and \( m_{2} \) are kept on a smooth horizontal surface. A spring of mass \( m \) and natural length \( L_{0} \) connects the two blocks as shown in the figure. At \( t=0, m_{1} \) and \( m_{2} \) are given velocities \( v_{1} \) and \( v_{2} \) as shown. Just after \( t=0 \), what is the value of \( \boldsymbol{x} \), so that the point \( \boldsymbol{P} \) remains at rest?
(a) \( \frac{L_{0} v_{1}}{v_{1}+v_{2}} \)
(b) \( \frac{L_{0} v_{2}}{v_{1}+v_{2}} \)
(c) \( \frac{L_{0} m_{1}}{m_{1}+m_{2}} \)
(d) \( \frac{L_{0} m_{2}}{m_{1}+m_{2}} \)
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