A particle executes SHM. Its velocities are v1 and v2 at displacements x1 and x2 from mean position respectively. The frequency of oscillation will be:

v1=ωA2-x12 and v2=ωA2-x22 v12-v22=ω2x22-x12⇒f=12πv12-v22x22-x12

A particle executes SHM. Its velocities are v1 and v2 at displacements x1 and x2 from mean position respectively. The frequency of oscillation will be:

v1=ωA2-x12 and v2=ωA2-x22 v12-v22=ω2x22-x12⇒f=12πv12-v22x22-x12

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A particle executes SHM. Its velocities are v₁ and v₂ at displacements x₁ and x₂ from mean position respectively. The frequency of oscillation will be:

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$\frac{1}{2 π} {[\frac{v_{1}^{2} - v_{2}^{2}}{x_{1}^{2} - x_{2}^{2}}]}^{\frac{1}{2}}$

$\frac{1}{2 π} {[\frac{v_{1}^{2} + v_{2}^{2}}{x_{2}^{2} + x_{1}^{2}}]}^{\frac{1}{2}}$

$\frac{1}{2 π} {[\frac{x_{1}^{2} - x_{2}^{2}}{v_{1}^{2} - v_{2}^{2}}]}^{\frac{1}{2}}$

$\frac{1}{2 π} {[\frac{x_{1}^{2} + x_{2}^{2}}{v_{1}^{2} + v_{2}^{2}}]}^{\frac{1}{2}}$

answer is B.

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$v_{1} = ω \sqrt{A^{2} - x_{1}^{2}} and v_{2} = ω \sqrt{A^{2} - x_{2}^{2}} v_{1}^{2} - v_{2}^{2} = ω^{2} (x_{2}^{2} - x_{1}^{2}) \Rightarrow f = \frac{1}{2 π} \sqrt{\frac{v_{1}^{2} - v_{2}^{2}}{x_{2}^{2} - x_{1}^{2}}}$

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A particle executes SHM. Its velocities are v1 and v2 at displacements x1 and x2 from mean position respectively. The frequency of oscillation will be:

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A particle executes SHM. Its velocities are v₁ and v₂ at displacements x₁ and x₂ from mean position respectively. The frequency of oscillation will be: