Figure 19 - A flat strip of steel

We shall assume that the strip is sufficiently long and the displace­ment sufficiently small so that the motion is essentially along a straight line. The mass of the strip itself is negligible.

Let the top of the strip be pulled to the right a distance A as in Figure 19 and released. The attached mass is then acted on by a re­storing force exerted by the steel strip and directed toward the equi­librium position O. It therefore accelerates in the direction of this force, and moves on toward the center with increasing speed. The rate of increase (i. e. the acceleration) is not constant, however, since the accelerating force becomes smaller as the body approaches the center.

When the body reaches the center the restoring force has decreased to zero, but because of the velocity which has been acquired, the body overshoots the equilibrium position and continues to move to­ward the left.

As soon as the equilibrium position is passed the restoring force again comes into play directed now toward the right. The body therefore decelerates and it will therefore be brought to rest at some point to the left of O, and repeat its motion in the opposite direction.

Both experiment and theory show that the motion will be con­fined to a range + A on either side of the equilibrium position, each to-and-fro movement taking place in the same length of time.

Were there no loss of energy by friction the motion would con­tinue indefinitely once it had been started. This type of motion, under the influence of an elastic restoring force and in the absence of all friction, is called simple harmonic motion, often abbreviated SHM.

Any sort of motion which repeats itself in equal intervals of time is called periodic, and if the motion is back and forth over the same path it is also called oscillatory.

A complete vibration or oscillation means one round trip, say from α to b and back to α.

The periodic time, or simply the period of the motion, represented by T, is the time required for one complete vibration.

The frequency, f, is the number of complete vibrations per unit time.

Evidently the frequency is the reciprocal of the period or

T = l: f

The displacement, x, at any instant, is the distance away from the equilibrium position or center of the path at that instant.

The amplitude, A, is the maximum displacement. The total range of the motion is therefore 2 A [2, С. 56 - 57].

2.5.8 Notes to text 2.5.7:

· to bring into play - привести в действие;

· to come into play – начать действовать;

· to bring to rest – остановить;

· the body overshoots the equilibrium position - тело переходит за пределы положения равновесия.