VISUALISASI FENOMENA HARMONIS DAN CHAOS PADA GETARAN TERGANDENG BERBASIS KOMPUTASI NUMERIK RUNGE KUTTA

VISUALIZATION OF HARMONIC AND CHAOS PHENOMENA IN COLLECTED VIBRATION BASED ON NUMERICAL COMPUTATION RUNGE KUTTA

Abstract

Research has been carried out on the visualization of harmonic and chaos phenomenont on coupled vibration physcal case using the Runge Kutta numerical computation method with the aim of applying the first to fourth order Runge Kutta computation method to obtain  a second order differential equation solution on coupled vibration system, calculating the displacement value of objects using computation method Runge Kutta order first to fourth, obtained a graph of the displacement of objects againts time in case of coupled vibration for harmonic and chaos states at certain step width values and compare the convergence of the Runge Kutta method from first to fourth order with the special analytical method. The solution of coupled vibration equation which is classified as a second order differential equation was quite difficulted to solve analytically, so the Runge Kutta computation method was used to solve it as an alternative solution. The results of the research showed that the harmonic state of the system was obtained when the displacement graph showed the motion of each pendulum which was constant with the pendulum displacement position with respect to time in the form of a sinusoidal graph at a value of C₁ = 40 N/m, C₂ = 30 N/m, C = 10 N/m, C = 0 N/m and the chaotic state was represented by a graph of the displacement of the pendulum with respect to time with an irregular pattern. In this case, it was found that the fourth order Runge Kutta method converged faster than the first to third order Runge Kutta method with the best results obtained at a step width value of 0,001. The fourth order Runge Kutta method also has a smaller approximation average error value  from first to third order Runge Kutta method was  on the fourth order Runge Kutta method and the avarage error values are , and  on the Runge Kutta method of first to third order.