With that in mind, the text goes on to elaborate further, calling attention to a figure that has an object suspended from a spring. The object has a rest position (point B), a maximum up displacement position (point A), and a maximum down displacement position (point C). The text says:
Simple harmonic motion is a special kind of vibrational motion in which the acceleration a of the object is directly proportional to the negative of its displacement d from its rest position. That is,
a = -kd.
The problem is that there is also a figure that shows the sinosoidal shape of the displacement (from rest) with respect to time. The sinosoidal waveform seems to demonstrate the exact opposite of what the text is asserting! Specifically, the object is exhibing the MOST acceleration when the displacement is least (near rest). I corrolate the slope of the sinosoidal waveform with the acceleration of the object, and the slope changes the most when the object is moving through its rest position. The acceleration is LEAST when the object is at maximum displacement (corresponding to the maximum and minimum parts of the sinosoidal, when the slope slows to near zero).
For example, when the mass hanging from the spring in Figure 43 is pulled down from its rest position B to the point C, the force of the spring tries to restore the mass to its rest position. Assuming that there is no frictional force to retard the motion, the amplitude will remain constant. The force increases in direct proportion to the distance that the mass is pulled from its rest position. Since the force increases directly, the acceleration of the mass of the object must do likewise, because (by Newton's Second Law of Motion) force is directly proportional to acceleration. As a result, the acceleration of the object varies directly with its displacement, and the motion is an example of simple harmonic motion.