While completing its third oscillation during linear S.H.M., a particle is at x = -√3/2·A, heading to the mean

Worked Examples · Example 5.2

Q. While completing its third oscillation during linear S.H.M., a particle is at x = -\sqrt3/2\cdotA, heading to the mean position. Determine the phase angle.

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A sin θ₁ = -√3/2 A with heading-to-mean gives θ₁ = 2π - π/3; third oscillation adds 2(2π): θ = 4π + (2π - π/3) = 17π/3.

From x = A sin θ₁ = -(√3/2)A, θ₁ is in the fourth quadrant (negative side, heading toward the mean position):

$\theta_1 = \left(2\pi - \frac{\pi}{3}\right)^c$ …

Q.While completing its third oscillation during linear S.H.M., a particle is at x = -√3/2·A, heading to the mean position. Determine the phase angle.