A particle executing harmonic motion is having velocities v1 and v2 at distance x1 and x2…

Physics · JEE Advanced · NTA ExamsOscillations and Waves

A particle executing harmonic motion is having velocities v1 and v2 at distance x1 and x2 from the equilibrium position. The amplitude of the motion is
  1. \(\sqrt{\frac{v_{1}^{2} x_{2}^{2}-v_{2}^{2} x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}\)
  2. \(\sqrt{\frac{v_{1}^{2} x_{1}^{2}-v_{2}^{2} x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}\)
  3. \(\sqrt{\frac{v_{1}^{2} x_{2}^{2}-v_{2}^{2} x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}\)
  4. \(\sqrt{\frac{v_{1}^{2} x_{2}^{2}+v_{2}^{2} x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}\)

Answer

(C) v_ 1 ^ 2 x_ 2 ^ 2 -v_ 2 ^ 2 x_ 1 ^ 2 v_ 1 ^ 2 -v_ 2 ^ 2

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