Mathematics

Di dalam matematika, bukti adalah serangkaian argumen logis yang menjelaskan kebenaran suatu pernyataan. Argumen-argumen ini dapat berasal dari premis pernyataan itu sendiri, teorema-teorema lainnya, definisi, dan akhirnya dapat berasal dari postulat dimana sistem matematika tersebut berasal. Yang dimaksud logis di sini, adalah semua langkah pada setiap argumen harus dijustfikasi oleh langkah sebelumnya. Jadi kebenaran semua premis pada setiap deduksi sudah dibuktikan atau diberikan sebagai asumsi.

This research constructs mathematic model for string vibration on Sasando that expressed as a second-order linear partial differential equation with u denote the vertical displacement experienced by the string at the point x at time t. Besides, the purpose of this research is to determine analytical solution using a method known as separation of variable. There are three analytical solutions from three cases based on constant coefficient values. Case 1 occurs when k d 2 > 4 n π l 2 1 2 c 2 + 2 c 2 l . Based on he simulation, the string produces a quarter wave within 3 seconds. This means the vibration wavelength 0.083 Hz. In this case the vertical displacement of the string is back to quiescent after vibrating to produce a quarter wave. Case 2 occurs when k d 2 = 4 n π l 2 1 2 c 2 + 2 c 2 l . The string produces 3.5 waves within 3 seconds, means the vibration wavelength is 1.67 Hz. In this case, the farthest vertical displacement (amplitude) become smaller drastically and back to...

The ZIKV model presented in this article is developed by modifying [1]’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order α to the stability of the model’s equilibrium point.