摘要
一個木塊連接一個彈簧在水平無摩擦表面上來回振盪是一種簡諧運動。一個小球在鉛直圓軌道上無摩擦運動就只是個週期運動，不是簡諧運動除非它的振幅很小。假如它們不是絕對光滑那運動將變得如何呢?在這篇文章裡我們企圖去解決有滑動摩擦的阻尼振盪。我們獲得一些初步的結果。對於前者我們有解析解，後者則得訴諸於數值計算。它們都存在一個「靜止區域」，那意謂著物體最後總是在那兒靜止下來。有阻尼的簡諧運動和理想狀況有相同的過期，但前者的振幅很有規律的遞減。至於鉛直的運動它的運動方程就較複雜，須要電腦的幫忙。我們用MATLAB套裝軟體寫程式，有興趣的讀者我們可以用電子郵件寄給你。
並列摘要
A block attached to a spring oscillates back and forth on a horizontal frictionless surface. It is a simple harmonic oscillation. A small ball moves without friction in a vertical circ1e track. It is merely a periodic motion, not a simple harmonic motion except small vibration. How to change the movement if they are not absolutely smooth? We attempt to the problem about damping oscillation with sliding friction in this paper. We obtain some preliminarγresu1ts. There is a analytic solution in the former case. We resort to numerical calculation in the latter case. There exists a ”stationary region”. It means that always keeps still down there finally. The damping simple harmonic oscillation has the same period with the ideal case. But the previous has descending amplitude with regularity. In the case of vertical motion the equation of motion is more complex. We need the help of computer. We write the program with MATLAB package. We can email the program to interested readers.
延伸閱讀
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- 姚志儒（2010）。摩擦制震壁之試驗與分析〔碩士論文，國立交通大學〕。華藝線上圖書館。https://doi.org/10.6842/NCTU.2010.00855
- 陳榕晟（2007）。長行程氣壓系統之摩擦力特性研究〔碩士論文，國立臺北科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0006-1807200714244100
- Zheng, Z. M., Ding, H. S., & N'Guerekata, G. M. (2013). Some Properties of Weighted Pseudo almost Periodic Functions. Abstract and Applied Analysis, 2013(), 561-568-353. https://doi.org/10.1155/2013/327213
- 許志鵬、陳威廷、楊子賸（2014）。Comparative analysis of the forging film coefficient of friction。鍛造，23(2)，36-40。https://www.airitilibrary.com/Article/Detail?DocID=1023750x-201407-201902140027-201902140027-36-40