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A particle is making simple harmonic motion along the \( \mathrm{X} \)-axis. If at a distances \( x_{1} \) and \( x_{2} \) from the mean position the velocities of the particle are \( v_{1} \) and \( v_{2} \) respectively. The time period of its oscillation is given as
(a) \( T=2 \pi \sqrt{\frac{x_{2}^{2}+x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}} \)
(b) \( T=2 \pi \sqrt{\frac{x_{2}^{2}+x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}} \)
(c) \( T=2 \pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}} \)
(d) \( T=2 \pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}} \)
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