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Two particles P and Q each perform SHM along the same straight line. Their displacements are given by y_P = A sin(omega*t + phi₁) and y_Q = A cos(omega*t + phi₂). At t = 0, particle P is at displacement A/sqrt(2) from mean position and moving toward positive displacement (rightward), while particle Q is at displacement (sqrt(3)/2)*A and moving toward negative displacement (leftward). What is the value of (phi₂ - phi₁)?

1. pi/12
2. 7*pi/12
3. 5*pi/12
4. None of the above

Correct answer: None of the above

Solution

From the conditions: phi₁ = pi/4 (P at A/sqrt(2), moving right) and phi₂ = pi/6 (Q at sqrt(3)A/2, moving left). Then phi₂ - phi₁ = pi/6 - pi/4 = -pi/12, which does not match any of the listed positive values.

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