A particle moving with SHM from an extremity of the path towards centre is observed to be at distances x₁, x₂ and x₃ from the centre at the ends of three successive seconds. The period of SHM is:

• A

  $\frac{2\mathrm{\pi }}{{\cos }^{-1}\left({\displaystyle \frac{{\mathrm{x}}_1+{\mathrm{x}}_3}{2{\mathrm{x}}_2}}\right)}$

• B

  $\frac{2\mathrm{\pi }}{{\cos }^{-1}\left({\displaystyle \frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2{\mathrm{x}}_3}}\right)}$

• C

  $\frac{2\mathrm{\pi }}{{\cos }^{-1}\left({\displaystyle \frac{{\mathrm{x}}_1+{\mathrm{x}}_3}{{\mathrm{x}}_2}}\right)}$

• D

  $\frac{2\mathrm{\pi }}{{\cos }^{-1}\left({\displaystyle \frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{{\mathrm{x}}_3}}\right)}$