(一)y''+λy=0, y(0)=0, y(10)=0 (12 分)

(二)(y'/x)'+(λ+1)y/x3=0, y(1)=0, y(eπ )=0 (13 分)

二、A sinusoidal voltage \( E \sin \omega t \), where \( t \) is time, is passed through a half-wave rectifier that clips the negative portion of the wave. Find the Fourier series of the resulting period function. \[ u(t) = \begin{cases} 0 & \text{if } -L < t < 0 \\ E \sin \omega t & \text{if } 0 < t < L \end{cases} \quad p = 2L = \frac{2\pi}{\omega} \]

三、請以史帝芬－波茲曼(Stefan-Boltzmann)公式，說明幅射熱熱傳特性(10 分)，並針對設備測試、系統功能及性能設計方面，提出 3 種在防火工程(Fire Safety Engineering)上的運用情境(15 分)。

四、請針對以下火羽在溫度層化環境下(Plumes in Temperature - StratifiedAmbients)的描述，解讀附圖的物理現象。火災科學 1原文：When a buoyant, turbulent plume rises, it cools by entrainment ofambient air. If the ambient air increases in temperature with height, which isnormal in buildings, and the fire source is weak, the temperature differencebetween the plume and the ambient, which gives the plume buoyancy, mayvanish and actually reverse in sign. Eventually the plume ceases to rise.Figure: Theoretical behavior of centerline plume variables in linearlytemperature-stratified ambients. Curve A: ratio of temperature rises (stratifiedversus unstratified), Curve B: ratio of axial velocities. Curve C: ratio of plumeradii. Curve D: ratio of volumetric species concentrations. Where z: heightabove top of combustible (m) and Zm: maximum vertical penetration of plumefluid in stratified ambient (m)火災科學 2

115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所：火災科學#139854

114年 - 114 中央警察大學_碩士班入學考試試題_消防科學研究所：火災科學#146884

112年 - 112 中央警察大學_碩士班入學考試試題_消防科學研究所：火災科學#147976

110年 - 110 中央警察大學_碩士班招生考試_消防科學研究所：火災科學#102957