Simple harmonic motion

When blood is ejected from the heart during systole, the pressure in the aorta and other large arteries rises, and then during diastole it falls again. The pressure rise is associated with outward motions of the walls, and they subsequently return because they are elastic. This process occurs during every cardiac cycle, and it can be seen that elements of the vessel walls oscillate cyclically, with a frequency of oscillation equal to that of the heartbeat. The blood, too, flows in a pulsatile manner, in response to the pulsatile pressure. In fact, as we shall see in Chapter 12, a pressure wave is propagated down the arterial tree. It is therefore appropriate in this chapter to consider the mechanics of pulsatile phenomena in general, and the propagation of waves in particular.

Let us examine first the oscillatory motion of a single particle. Suppose that the particle can be in equilibrium at a certain point, say P, but when it is disturbed from this position, it experiences a restoring force, tending to return it to P. There are many examples of this situation, as when a particle is hanging from a string and is displaced sideways (a simple pendulum) or when the string is elastic and the particle is pulled down below its equilibrium position. In cases like these, the restoring force increases as the distance by which the particle is displaced from P increases. In fact, for sufficiently small displacements, the restoring force is approximately proportional to the distance from P (see p. 124). If the particle is displaced and then released, it will return towards P, but will overshoot because of its inertia.