Find out now, what determines the period of oscillation of the mathematical pendulum. With experience on the model of mathematical pendulum is easy to install, its vibrations are damped. Experience has shown, what is the period of oscillation of the pendulum when the damping is not changed, t. e. it does not depend on amplitude (at small angles of swing). This property of the pendulum was opened by Mr.. Galileo and is called isochronism (ravnoudalennostj). Experience shows, what is the period of oscillation of a pendulum does not depend on its mass.

Using the formula (24.12) show, what is the period of oscillation of a pendulum depends on its length l. Since with increasing l, the restoring force F decreases, decreases and the acceleration of motion of a pendulum, and, therefore, the period of oscillation increases. From the same equation it can be seen, if you increase g grows F_in, so, the period decreases.

Describes the properties of the mathematical pendulum formulated in the form two laws.

• At small angles of swing, the period of oscillation of the mathematical pendulum does not depend on the amplitude, or the mass of the pendulum.
• The period of oscillation of the mathematical pendulum is directly proportional to the square root of the length of the pendulum l and back proportional to the square root of the gravitational acceleration g:

T = 2π√(l/g) (24.13)

The formula (24.13) can be obtained from (24.10) and (24.4), given, for the pendulum k=mg/l.

Note, the half of the complete oscillation is called p R o s-t s m swing, for example, the movement of the pendulum from one extreme position to the other. Since the period of simple oscillations T_p= T/2, the formula to calculate the period of oscillations the simple pendulum has the form:

T_p = π√(l/g) (24.14)