CALCULATION AND VISUALIZATION OF SMALL OSCILLATIONS OF A DOUBLE PLANE PENDULUM

The article considers the calculation and visualization of small oscillations of a double plane simple pendulum. It contains the brief derivation of the motion equation and its solutions; the mathematical model of the motion in the form of the system of nonlinear differential equations. Experiments with the double pendulum are performed at various ratios of bodies' masses and initial angles, in particular for three values of mu = m(1)/m(2) : mu(1)= 0.1, mu(2)= 0.2, mu(3)= 0.3 when the lengths of the pendulum are l = l(1) = l(2) = 0.25m and g = 9.8 m/s(2). The angles of pendulum deviation are given in radians. The graphs of small oscillations of the pendulum show that beats occur in the system during which energy cyclically passes from one pendulum to another. When one pendulum almost stops, the other pendulum is at its maximum amplitude. After a while pendulums "exchange their states" and so on. Oscillations with a bigger frequency omega(1) are modulated by lower frequency oscillations with a frequency omega(2).