Figure 2 shows the motion typical of the SHO system, plotting the position of the mass x(t) along the vertical axis as a function of time t along the horizontal axis. We shall use the following quantities to characterize this motion.
, also equal to one-half
of the total range of motion 
.
: the time
elapsed 
since the most recent occurrence of the maximum
displacement in the motion ( 
), measured in
radians where we associate 
of phase with each
cycle. Thus, 
.
: the phase of the oscillator at
time t=0, 
.
Note that with the above definitions, we can write down the motion immediately as
Figure 2: Simple harmonic motion: position x(t) (solid curve),
equilibrium position 
(dotted line), amplitude A (vertical
dashed line), time elapsed since the most recent maximum as
appears in the definition of the initial phase (horizontal
dashed arrow).
