Answer:
The general equation for S.H.M. is \[y=A\sin (\omega t+{{\phi }_{0}})\] As the displacement is half of the amplitude \[(y=A/2),\]so \[A/2=A\sin (\omega t+{{\phi }_{0}})\] or \[\sin (\omega t+{{\phi }_{0}})=\frac{1}{2}\] \[\therefore \] \[\omega t+{{\phi }_{0}}={{30}^{\circ }}\] or \[{{150}^{\circ }}\] As the two particles are going in opposite directions, the phase of one is \[\text{3}0{}^\circ \] and that of the other \[\text{15}0{}^\circ \] Hence the phase difference between the two particles \[=150-30=\mathbf{12}{{\mathbf{0}}^{\mathbf{o}}}\]
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