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カジヤマ ユウジ
Yuji Kajiyama
梶山 裕二 所属 教育学部 職種 准教授 |
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| 言語種別 | 英語 |
| 発行・発表の年月 | 2022/06/01 |
| 形態種別 | 研究論文 |
| 査読 | 査読あり |
| 標題 | A State Equation Approach to Harmonic Oscillation |
| 執筆形態 | 共著 |
| 掲載誌名 | The Physics Educator |
| 掲載区分 | 国外 |
| 出版社・発行元 | World Scientific |
| 巻・号・頁 | 4(2),pp.2250007-1-2250007-8 |
| 総ページ数 | 8 |
| 著者・共著者 | Koichi Ban and Yuji Kajiyama |
| 概要 | We discuss the motion of a harmonic oscillator in a state equation approach commonly applied in a modern control theory (MCT) of engineering. Instead of a second-order differential equation as students learn in classes of mechanics, the state equation is written in a matrix form of a first-order differential equation of the state vector ${¥bf X}(t)=(x(t),¥dot x(t))^T$. We present the motion of a mass-spring-damper (MSD) system on an inclined plane and a simple pendulum in a viscous fluid. In the former case, we treat the gravitational force along the inclined plane as an input signal to the system. In the latter case, we treat the buoyant force and the drag force from the fluid as feedback to the system, controlling the final state of the system. The state equation approach presented in this article will help university students bridge the gap between physics and engineering. |