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Question:

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t=0, one particle has displacement A while the other one has displacement -A/2 and they are moving towards each other. If they cross each other at time t, then t is:

5T/6

T/3

T/4

T/6

Solution:

Equations of two particles can be written as x1 = Acos(ωt) and x2 = Asin(ωt - π/6). Equating the two gives t = T/6.