The composition of two simple harmonic motions of equal periods at right angles to each other and with a phase difference of π results in the displacement of the particle along

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(3) straight line. Given: x=A sin ω t and y=B sin(ω t+π), the same period, at right angles. sin(ω t+π)=-sin ω t, so y=-B sin ω t. Idea: look for a fixed relation between x and y rather than eliminating t through squares. y/x=-B/A at every instant. y=-B/Ax, a straight line through the origin with negative slope. So the particle moves back and forth along a straight line.

The composition of two simple harmonic motions of equal periods at right angles to each other and with a phase difference of π results in the displacement of the particle along

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