A particle is moving with SHM.If it has velocities of v₁ and v₂ when it is at positions x₁ and x₂ from the equilibrium position respectively,then the square of the frequency of vibration (f ²)is given by: A)(v₁² - v₂² )/ 4 $\pi$²(x₁² -x₂² ) B)(v₁² -v₂² )/ 4 $\pi$²(x₂² - x₁² ) C)(v₁² + v₂² )/ 4 $\pi$²(x₂² -x₁² ) D)(v₁² + v₂² )/ 2 $\pi$²(x₂² + x₁² ) E)(v₁² + v₂² )/ (x₂² - x₁² )

Question

Quizplus · Accepted Answer

The correct formula for the square of the frequency of vibration in simple harmonic motion (SHM) involves the difference in the squares of velocities divided by the difference in the squares of positions. This is because the frequency of vibration in SHM is related to the maximum velocity and the amplitude of motion, and the given velocities and positions are related through the conservation of energy in SHM. Option B correctly represents this relationship by subtracting the square of the velocity at one position from the square of the velocity at another position, and dividing by the difference in the squares of the positions, all multiplied by a constant factor.

A Particle Is Moving with SHM π\piπ 2 (x12 -X22 ) B)(v12 -V22 )/ 4

A Particle Is Moving with SHM $\pi$ ²(x₁² -X₂² )
B)(v₁² -V₂² )/ 4