{"cells":[{"cell_type":"markdown","metadata":{},"source":["<br />\n","\n","<div style=\"text-align: center;\">\n","<font size=\"7\">数値計算試験問題</font>\n","</div>\n","<br />\n","<div style=\"text-align: right;\">\n","<font size=\"4\">2020/12/18 実施</font>\n","<br />\n","<font size=\"4\">cc by Shigeto R. Nishitani 2020 </font>\n","</div>\n","\n"]},{"cell_type":"markdown","metadata":{},"source":["# fitting(25点)\n","\n","次のデータにフィットした二次関数を求め，データと同時に plot せよ.\n","\n","``` python\n","import numpy as np\n","\n","xdata = np.array([1,2,3,4])\n","ydata = np.array([1,8,9,10])\n","```"]},{"attachments":{"image.png":{"image/png":"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"}},"cell_type":"markdown","metadata":{},"source":["# fsolve(25点)\n","\n","次の関数\n","$$\n","f(x) = -\\left(\\frac{1}{x}\\right)^6+2\\,\\left(\\frac{1}{x}\\right)^{12}\n","$$\n","は図に示す通り，解$1.1224620483093721$を持つ．\n","![image.png](attachment:image.png)\n","\n","二分法とNewton法によって数値解を求めよ．\n","二分法の初期値は$x=1..2$，Newton法の初期値は$x=1$とし，\n","繰り返しは10回程度で求めよ．\n","収束の様子を片対数(logplot)で同時にプロットせよ．\n","\n","与関数$f(x)$ の微分は\n","``` python\n","def df(x):\n","    return (6.0/x**7.0)-(24.0/x**13.0)\n","```\n","で与えられる．\n","\n"]},{"cell_type":"markdown","metadata":{},"source":["# ode - oscillation(25点)\n","\n","Euler法を用いてバネ振動の常微分方程式を解く．\n","\n","規格化したバネ定数$k$を0.001として，\n","刻み幅dtを0.1秒とした場合に200秒までの振る舞いを\n","\n","``` python\n","def euler3(x0,v0):\n","  v1 = v0 +(- k * x0) * dt\n","  x1 = x0 + v0 * dt\n","  return [x1, v1]\n","\n","t, dt, k=0.0, 0.1, 0.001\n","tt,xx,vv=[0.0],[0.0],[0.1]\n","for i in range(0,2000):\n","```\n","でplotしてみよ．\n","\n","振動の周期$T$が\n","$$\n","f = \\frac{1}{2\\pi}\\sqrt{\\frac{k}{m}}\n","$$\n","\n","$$\n","T = \\frac{1}{f}\n","$$\n","と一致していることを確かめよ．\n","\n","ただし，$k$は規格化しているので，$m=1$\n","\n","\n","また，規格化したバネ定数$k$を0.01とした時，周期はいくらになるか．\n","また，200秒まででだいたい何周期になるか"]},{"cell_type":"markdown","metadata":{},"source":["# fft(25点)\n","\n","FFTによって周期62.831853のsin関数がどのように変換されるかを調べる．\n","```python\n","2*np.pi*(3*62.831853) = 1184\n","```\n","であることに注意して，\n","``` python\n","def func(x):\n","    return np.sin(x/62.831853)\n","\n","x = np.linspace(0, 1184, 1184)\n","```\n","をx=0..1184で実空間で表示せよ．\n","FFTに入れるチャンネル数(通常は256など)が1184+1の場合，\n","パワースペクトル(spectrum_power, FFTをかけた後の周波数強度)を求めて表示せよ．\n","パワースペクトルのピーク位置が何を意味するかを述べよ．"]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.8.3"},"toc":{"base_numbering":1,"nav_menu":{},"number_sections":true,"sideBar":true,"skip_h1_title":false,"title_cell":"Table of Contents","title_sidebar":"Contents","toc_cell":false,"toc_position":{},"toc_section_display":true,"toc_window_display":true}},"nbformat":4,"nbformat_minor":4}