# Phase relationship

In simple harmonic motion, the phase relationships between x, v and a are depicted in the following rotating vector diagram:

Actually, I don't understand how the left one can be drawn to the right one in the above three pictures, especially the +/- sign. Please kindly explain.

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The diagram on the right shows the various parameters, a,v and x, in a simple harmonic motion. Their magnitudes are given by the projection of each vector on the x-axis (i.e. the horizontal axis).

In the first diagram, for example, xo lies on the -ve x-axis at maximum magnitude. This shows that the oscillating object is at the left extreme position. The acceleration vector ao lies on the +ve x-axis. This shows that the acceleration is in opposite direction to the displacement xo, and has maximum magnitude. The velocity vector vo, has no projection on the x-axis, hence the velocity of the oscillating object is zero at that moment.

In the second diagram, both xo and ao have no projection on the x-axis, hence they are all zero in magnitude at that instant of time. The velocity vector vo lies completely on the x-axis, hence velocity is maximum and points in direction to the right.

Simialrly for the third diagram, which is just the reverse of the first diagram.