An elastic force tends always to bring the body back to the position of equilibrium; if the distance is not too great, the force is proportional to the elongation. A physical body is always under the influence of friction, the acceleration of which is opposite to the direction of the movement, and therefore diminishes the velocity. The form of the resulting movement depends on the amount of friction, and, roughly speaking, we may distinguish two types of elastic movements:[70] the first type is a periodic movement, the second an aperiodic. Let us suppose that a body is carried from its position of equilibrium by a sudden impulse, which transmits a certain velocity to the body. Friction and elasticity diminish this velocity, and after a certain time the body attains a maximum elongation, where the velocity is zero. Then the body returns under the influence of elasticity and under the retardation of friction. There are two cases possible, either the elastic force is strong enough to overcome friction and to carry the body over the position of equilibrium, or it is not strong enough. In the first case, it is easy to see, the body repeats the same form of movement on the other side of the position of equilibrium, and the conditions being constant a vibratory movement results as the stationary form. In the second case the body approaches the position of equilibrium asymptotically. The first case may be illustrated by the vibrations of a magnet needle suspended with little friction, the second by the movement of a door which is regulated by a well-working shutter. These forms of the movement of a body under the influence of elasticity and friction are illustrated in Fig. 3. Curve 1 shows a movement where friction is so small that it can be neglected; it is, of course, a simple sine curve. Curve 2 shows the effect of friction on vibrations. The period of damped vibrations is greater than in the frictionless movement, but the amplitudes are smaller. The amplitudes of a damped vibration decrease constantly and there is a simple relation between two subsequent amplitudes. The ratio between them is constant, and, therefore, if one amplitude and this constant ratio are known, all the other amplitudes can be calculated. The amplitudes of such a movement decrease as the terms of a geometric series. The dotted line in Fig. 4 represents the rapidity of this decrease. It is obvious that the smaller the constant ratio of two subsequent terms is, the more rapidly will the amplitudes decrease. This ratio depends on friction, and becomes smaller when friction becomes greater. A vibration under heavy friction dies out quickly. Curve 3 shows a movement where friction is too great to allow any vibrations. The body does not acquire a velocity which can carry it over the position of equilibrium, but it approaches this position with ever diminishing velocity. [Illustration: Figs. 3 and 4]