Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X0(X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is :

Engineering

Physics

Superposition of Simple Harmonic Motion

Question

Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X₀(X₀ > A). If the maximum separation between them is (X₀ + A), the phase difference between their motion is :

$\frac{π}{2}$

$\frac{π}{6}$

$\frac{π}{4}$

$\frac{π}{3}$

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x₁ = A sin(ωt + φ₁)

x₂ = A sin(ωt + f₂)

$x_{1} - x_{2} = A [2 \sin [ωt + \frac{ϕ_{1} + ϕ_{2}}{2}] \sin [\frac{ϕ_{1} - ϕ_{2}}{2}]]$

$A = 2 Asin (\frac{ϕ_{1} - ϕ_{2}}{2})$

$\frac{ϕ_{1} - ϕ_{2}}{2} = \frac{π}{6}$

$ϕ_{1} = \frac{π}{3}$