Using Differential Equation to Explain the Simple Harmonic Motion Equation

Abstract

It aims to explain the motion law of simple harmonic vibration in phase space with the complex part of differential equation. Introduce and enumerate differential equations, classify and discuss each case, and finally get the appropriate formula. Angular velocity, phase, displacement, time, amplitude, acceleration and trigonometric function are connected by equation solution. It explains the rationality of physics in phase space, and does not restrict the limited operation with real space. Using the knowledge of second order differential equation, the formula of angular velocity of simple harmonic motion is successfully proved. According to the equation of motion, Displacement is a cosine function with respect to time t; The velocity is a sine function with respect to time t; and the acceleration is a sine function with respect to time t of two angular velocity multiples. The emergence of differential equations is equivalent to opening up a new way for the scientific community, so many problems in other disciplines need to be solved and proved. Therefore, it is a very reasonable behavior to combine physics with this method.