{"id":6060,"date":"2024-01-08T22:02:02","date_gmt":"2024-01-08T13:02:02","guid":{"rendered":"https:\/\/now0930.pe.kr\/wordpress\/?p=6060"},"modified":"2026-10-04T08:23:28","modified_gmt":"2026-10-03T23:23:28","slug":"laplace-transform2","status":"publish","type":"post","link":"https:\/\/now0930.pe.kr\/wordpress\/laplace-transform2\/","title":{"rendered":"Laplace Transform2"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"448\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/laplace-transform-img1652263785631-45.JPG-rs-high-webp.webp\" alt=\"\" class=\"wp-image-6061\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/byjusexamprep.com\/gate-eee\/laplace-transform#toc-2\">https:\/\/byjusexamprep.com\/gate-eee\/laplace-transform#toc-2<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/xlinux.nist.gov\/dads\/HTML\/gammaFunction.html\"><strong>Definition:<\/strong> The gamma function of n, written \u0393(n), is \u222b <sub>0<\/sub><sup>\u221e<\/sup> e<sup>-x<\/sup>x<sup>n-1<\/sup>dx. Recursively \u0393(n+1) = n\u0393(n). For non-negative integers \u0393(n+1) = <em>n!<\/em>.<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-3.png\" alt=\"\" class=\"wp-image-6065\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-3.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-3-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image.png\" alt=\"\" class=\"wp-image-6062\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-1.png\" alt=\"\" class=\"wp-image-6063\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-1.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-1-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-2.png\" alt=\"\" class=\"wp-image-6064\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-2.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-2-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/03\/\uc81c\ubaa9-\uc5c6\uc74c-1-22.jpg\" alt=\"\" class=\"wp-image-6964\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/03\/\uc81c\ubaa9-\uc5c6\uc74c-1-22.jpg 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/03\/\uc81c\ubaa9-\uc5c6\uc74c-1-22-768x1050.jpg 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n&#8220;`html\n<div class=\"chapter19-wide\">\n\n  <h1>Laplace Transform 2<\/h1>\n\n  <div class=\"subtitle\">\n    Laplace Transform Table \u00b7 Gamma Function \u00b7 Frequency Shift \u00b7 Time Delay \u00b7 \ubbf8\ubd84 \u00b7 \uc801\ubd84\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>1. \uae30\ubcf8 Laplace Transform Table<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"table-wrap\">\n\n      <table>\n\n        <thead>\n          <tr>\n            <th>f(t)<\/th>\n            <th>\u2112{f(t)}<\/th>\n          <\/tr>\n        <\/thead>\n\n        <tbody>\n\n          <tr>\n            <td>1<\/td>\n            <td>1\/s<\/td>\n          <\/tr>\n\n          <tr>\n            <td>e<sup>at<\/sup><\/td>\n            <td>1\/(s-a)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>t<sup>n<\/sup><\/td>\n            <td>n!\/s<sup>n+1<\/sup><\/td>\n          <\/tr>\n\n          <tr>\n            <td>sin at<\/td>\n            <td>a\/(s<sup>2<\/sup>+a<sup>2<\/sup>)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>cos at<\/td>\n            <td>s\/(s<sup>2<\/sup>+a<sup>2<\/sup>)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>sinh at<\/td>\n            <td>a\/(s<sup>2<\/sup>-a<sup>2<\/sup>)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>cosh at<\/td>\n            <td>s\/(s<sup>2<\/sup>-a<sup>2<\/sup>)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>e<sup>at<\/sup>t<sup>n<\/sup><\/td>\n            <td>\n              n!\/(s-a)<sup>n+1<\/sup>\n            <\/td>\n          <\/tr>\n\n          <tr>\n            <td>e<sup>at<\/sup>cos bt<\/td>\n            <td>\n              (s-a)\/[(s-a)<sup>2<\/sup>+b<sup>2<\/sup>]\n            <\/td>\n          <\/tr>\n\n          <tr>\n            <td>e<sup>at<\/sup>sin bt<\/td>\n            <td>\n              b\/[(s-a)<sup>2<\/sup>+b<sup>2<\/sup>]\n            <\/td>\n          <\/tr>\n\n          <tr>\n            <td>f'(t)<\/td>\n            <td>sF(s)-f(0)<\/td>\n          <\/tr>\n\n          <tr>\n            <td>f&#8221;(t)<\/td>\n            <td>\n              s<sup>2<\/sup>F(s)-sf(0)-f'(0)\n            <\/td>\n          <\/tr>\n\n          <tr>\n            <td>\n              \u222b<sub>0<\/sub><sup>t<\/sup> f(u)du\n            <\/td>\n            <td>F(s)\/s<\/td>\n          <\/tr>\n\n          <tr>\n            <td>t<sup>n<\/sup>f(t)<\/td>\n            <td>\n              (-1)<sup>n<\/sup>\n              d<sup>n<\/sup>F(s)\/ds<sup>n<\/sup>\n            <\/td>\n          <\/tr>\n\n          <tr>\n            <td>e<sup>at<\/sup>f(t)<\/td>\n            <td>F(s-a)<\/td>\n          <\/tr>\n\n        <\/tbody>\n\n      <\/table>\n\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>2. t<sup>n<\/sup>\uc758 Laplace Transform<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc815\uc758\uc5d0\uc11c \uc9c1\uc811 \uacc4\uc0b0\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{t<sup>n<\/sup>}\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      t<sup>n<\/sup>e<sup>-st<\/sup>dt\n    <\/div>\n\n    <p>\n      \ubd80\ubd84\uc801\ubd84\uc744 \uc801\uc6a9\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u222b f&#8217;g dt\n      =\n      fg\n      &#8211;\n      \u222b fg&#8217; dt\n    <\/div>\n\n    <p>\n      \ub2e4\uc74c\uacfc \uac19\uc774 \ub450\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      f = t<sup>n<\/sup>\n    <\/div>\n\n    <div class=\"formula\">\n      dg = e<sup>-st<\/sup>dt\n    <\/div>\n\n    <div class=\"formula\">\n      g\n      =\n      -1\/s \u00b7 e<sup>-st<\/sup>\n    <\/div>\n\n    <p>\n      \ubd80\ubd84\uc801\ubd84 \uacb0\uacfc\n    <\/p>\n\n    <div class=\"formula\">\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      t<sup>n<\/sup>e<sup>-st<\/sup>dt\n      =\n      (n\/s)\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      t<sup>n-1<\/sup>e<sup>-st<\/sup>dt\n    <\/div>\n\n    <p>\n      \uc774\ub97c \ubc18\ubcf5\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{t<sup>n<\/sup>}\n      =\n      n!\/s<sup>n+1<\/sup>\n    <\/div>\n\n    <div class=\"table-wrap\">\n\n      <table>\n        <thead>\n          <tr>\n            <th>\uc2dc\uac04\ud568\uc218<\/th>\n            <th>Laplace Transform<\/th>\n          <\/tr>\n        <\/thead>\n\n        <tbody>\n\n          <tr>\n            <td>1<\/td>\n            <td>1\/s<\/td>\n          <\/tr>\n\n          <tr>\n            <td>t<\/td>\n            <td>1\/s<sup>2<\/sup><\/td>\n          <\/tr>\n\n          <tr>\n            <td>t<sup>2<\/sup><\/td>\n            <td>2\/s<sup>3<\/sup><\/td>\n          <\/tr>\n\n          <tr>\n            <td>t<sup>3<\/sup><\/td>\n            <td>6\/s<sup>4<\/sup><\/td>\n          <\/tr>\n\n        <\/tbody>\n      <\/table>\n\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>3. Gamma Function<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc774\ubbf8\uc9c0\uc5d0\uc11c\ub294 t<sup>n<\/sup>\uc758 Laplace Transform\uc744\n      Gamma Function\uacfc \uc5f0\uacb0\ud558\uc5ec \uc815\ub9ac\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u0393(n)\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      x<sup>n-1<\/sup>e<sup>-x<\/sup>dx\n    <\/div>\n\n    <div class=\"formula\">\n      \u0393(n+1)\n      =\n      n\u0393(n)\n    <\/div>\n\n    <p>\n      \uc815\uc218 n\uc5d0 \ub300\ud574\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      \u0393(n+1) = n!\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      x<sup>n<\/sup>e<sup>-x<\/sup>dx\n      =\n      n!\n    <\/div>\n\n    <p>\n      \uc774 \uad00\uacc4\ub97c \uc774\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{t<sup>n<\/sup>}\n      =\n      n!\/s<sup>n+1<\/sup>\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        factorial n!\uacfc Gamma Function\uc774 \uc5f0\uacb0\ub418\ubbc0\ub85c\n        t\uc758 \uac70\ub4ed\uc81c\uacf1\uc5d0 \ub300\ud55c Laplace Transform\uc744\n        \uc77c\ubc18\uc2dd\uc73c\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>4. Frequency Shift<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\ud568\uc218 f(t)\uc758 Laplace Transform\uc744 F(s)\ub77c\uace0 \ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      f(t)\n      \u2194\n      F(s)\n    <\/div>\n\n    <p>\n      \uc2dc\uac04\ud568\uc218\uc5d0 e<sup>at<\/sup>\ub97c \uacf1\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{e<sup>at<\/sup>f(t)}\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      f(t)e<sup>at<\/sup>e<sup>-st<\/sup>dt\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      f(t)e<sup>-(s-a)t<\/sup>dt\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>at<\/sup>f(t)\n      \u2194\n      F(s-a)\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c e<sup>at<\/sup>\ub97c \uacf1\ud558\uba74\n        s-domain\uc5d0\uc11c\ub294 s\uac00 s-a\ub85c \uc774\ub3d9\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>5. e<sup>at<\/sup>t<sup>n<\/sup><\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uae30\ubcf8 \uad00\uacc4\n    <\/p>\n\n    <div class=\"formula\">\n      t<sup>n<\/sup>\n      \u2194\n      n!\/s<sup>n+1<\/sup>\n    <\/div>\n\n    <p>\n      \uc5d0 Frequency Shift\ub97c \uc801\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>at<\/sup>t<sup>n<\/sup>\n      \u2194\n      n!\/(s-a)<sup>n+1<\/sup>\n    <\/div>\n\n    <p>\n      \uc989 s \ub300\uc2e0 s-a\ub97c \ub300\uc785\ud558\uba74 \ub41c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      s\n      \u2192\n      s-a\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>6. \ubbf8\ubd84\uc758 Laplace Transform<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c \ubbf8\ubd84\ud558\uba74\n      s-domain\uc5d0\uc11c\ub294 s\uac00 \uacf1\ud574\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{f'(t)}\n      =\n      sF(s)-f(0)\n    <\/div>\n\n    <p>\n      \ucd08\uae30\uc870\uac74\uc774 0\uc774\ub77c\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{f'(t)}\n      =\n      sF(s)\n    <\/div>\n\n    <p>\n      2\ucc28 \ubbf8\ubd84\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{f&#8221;(t)}\n      =\n      s<sup>2<\/sup>F(s)\n      &#8211;\n      sf(0)\n      &#8211;\n      f'(0)\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \uc2dc\uac04\uc601\uc5ed\uc758 \ubbf8\ubd84\uc740\n        s-domain\uc5d0\uc11c s\uc758 \uacf1\uc148\uc73c\ub85c \ubcc0\ud658\ub41c\ub2e4.\n        \ub2e8, \ucd08\uae30\uc870\uac74 \ud56d\uc774 \ucd94\uac00\ub41c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>7. \uc801\ubd84\uc758 Laplace Transform<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c \uc801\ubd84\ud558\uba74\n      s-domain\uc5d0\uc11c\ub294 1\/s\uac00 \uacf1\ud574\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{\n      \u222b<sub>0<\/sub><sup>t<\/sup>\n      f(u)du\n      }\n      =\n      F(s)\/s\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \ubbf8\ubd84 \u2194 s \uacf1\uc148\n        <br><br>\n        \uc801\ubd84 \u2194 1\/s \uacf1\uc148\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>8. sin at\uc640 cos at<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      sin at\n      \u2194\n      a\/(s<sup>2<\/sup>+a<sup>2<\/sup>)\n    <\/div>\n\n    <div class=\"formula\">\n      cos at\n      \u2194\n      s\/(s<sup>2<\/sup>+a<sup>2<\/sup>)\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        sin\uc740 \ubd84\uc790\uc5d0 a,\n        cos\ub294 \ubd84\uc790\uc5d0 s\uac00 \uc704\uce58\ud55c\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>9. Time Delay<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc6d0\ub798 \uc2e0\ud638\uac00\n    <\/p>\n\n    <div class=\"formula\">\n      f(t)\n      \u2194\n      F(s)\n    <\/div>\n\n    <p>\n      \uc77c \ub54c \uc2e0\ud638\uac00 \u03bb\ub9cc\ud07c \uc9c0\uc5f0\ub418\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      f(t-\u03bb)\n    <\/div>\n\n    <p>\n      Laplace Transform\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-s\u03bb<\/sup>F(s)\n    <\/div>\n\n    <p>\n      \uac00 \ub41c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      f(t-\u03bb)\n      \u2194\n      e<sup>-s\u03bb<\/sup>F(s)\n    <\/div>\n\n    <p>\n      \ubcc0\uc218\ubcc0\ud658\n    <\/p>\n\n    <div class=\"formula\">\n      z = t-\u03bb\n    <\/div>\n\n    <div class=\"formula\">\n      t = z+\u03bb\n    <\/div>\n\n    <p>\n      \ub97c \uc0ac\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-s(z+\u03bb)<\/sup>\n      =\n      e<sup>-sz<\/sup>\n      e<sup>-s\u03bb<\/sup>\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c \uc2dc\uac04\uc9c0\uc5f0 \ud56d\n      e<sup>-s\u03bb<\/sup>\uac00 \ub098\ud0c0\ub09c\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>10. Time Delay\uc640 \uc81c\uc5b4\uc2dc\uc2a4\ud15c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ud544\uae30\uc5d0\uc11c\ub294 \uc2dc\uac04\uc9c0\uc5f0\uc774\n      \uc81c\uc5b4\uc2dc\uc2a4\ud15c\uc5d0 \ubbf8\uce58\ub294 \uc601\ud5a5\uc744 \uc815\ub9ac\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-s\u03bb<\/sup>F(s)\n    <\/div>\n\n    <p>\n      \uc8fc\ud30c\uc218\uc751\ub2f5\uc5d0\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      s = j\u03c9\n    <\/div>\n\n    <p>\n      \ub85c \ub450\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-j\u03c9\u03bb<\/sup>\n    <\/div>\n\n    <p>\n      Euler \uad00\uacc4\ub97c \uc0ac\uc6a9\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-j\u03c9\u03bb<\/sup>\n      =\n      cos(\u03c9\u03bb)\n      &#8211;\n      j sin(\u03c9\u03bb)\n    <\/div>\n\n    <p>\n      \ud06c\uae30\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      |e<sup>-j\u03c9\u03bb<\/sup>| = 1\n    <\/div>\n\n    <p>\n      \uc704\uc0c1\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      \u2220e<sup>-j\u03c9\u03bb<\/sup>\n      =\n      -\u03c9\u03bb\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0\uc740 \uc8fc\ud30c\uc218\uc751\ub2f5\uc758 \ud06c\uae30\ub294 \ubcc0\ud654\uc2dc\ud0a4\uc9c0 \uc54a\uace0,\n        \uc704\uc0c1\uc744 -\u03c9\u03bb\ub9cc\ud07c \uc9c0\uc5f0\uc2dc\ud0a8\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>11. Time Delay\uc640 Phase Margin<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2dc\uac04\uc9c0\uc5f0 \uc694\uc18c\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>-s\u03bb<\/sup>\n    <\/div>\n\n    <p>\n      \ub294 \uc8fc\ud30c\uc218\uc601\uc5ed\uc5d0\uc11c \ucd94\uac00 \uc704\uc0c1\uc9c0\uc5f0\n    <\/p>\n\n    <div class=\"formula\">\n      -\u03c9\u03bb\n    <\/div>\n\n    <p>\n      \uc744 \ubc1c\uc0dd\uc2dc\ud0a8\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      Magnitude = 1\n    <\/div>\n\n    <div class=\"formula\">\n      Phase = -\u03c9\u03bb\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c \uac19\uc740 gain\uc744 \uc720\uc9c0\ud558\uba74\uc11c\n      \uc8fc\ud30c\uc218\uac00 \uc99d\uac00\ud560\uc218\ub85d \uc704\uc0c1\uc9c0\uc5f0\uc740 \ucee4\uc9c4\ub2e4.\n    <\/p>\n\n    <div class=\"warning\">\n      <strong>\n        \uc2dc\uac04\uc9c0\uc5f0\uc774 \uc99d\uac00\ud558\uba74 \ucd94\uac00\uc801\uc778 \uc704\uc0c1\uc9c0\uc5f0\uc774 \ubc1c\uc0dd\ud558\ubbc0\ub85c\n        Phase Margin\uc774 \uac10\uc18c\ud560 \uc218 \uc788\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>12. e<sup>-t<\/sup> \uc608\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ud544\uae30 \uc608\uc81c\uc5d0\uc11c\ub294\n    <\/p>\n\n    <div class=\"formula\">\n      f(t) = e<sup>-t<\/sup>\n    <\/div>\n\n    <p>\n      \uc758 Laplace Transform\uc744 \uc815\uc758\uc5d0\uc11c \uacc4\uc0b0\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u2112{e<sup>-t<\/sup>}\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      e<sup>-t<\/sup>e<sup>-st<\/sup>dt\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      \u222b<sub>0<\/sub><sup>\u221e<\/sup>\n      e<sup>-(s+1)t<\/sup>dt\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      1\/(s+1)\n    <\/div>\n\n    <p>\n      \uc77c\ubc18\uc2dd\n    <\/p>\n\n    <div class=\"formula\">\n      e<sup>at<\/sup>\n      \u2194\n      1\/(s-a)\n    <\/div>\n\n    <p>\n      \uc5d0\uc11c a=-1\uc744 \ub300\uc785\ud55c \uacb0\uacfc\uc640 \ub3d9\uc77c\ud558\ub2e4.\n    <\/p>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>13. \uc774\ubbf8\uc9c0 \ud575\uc2ec \uacf5\uc2dd \uc815\ub9ac<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n\n      <thead>\n        <tr>\n          <th>\ud56d\ubaa9<\/th>\n          <th>\uad00\uacc4\uc2dd<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n\n        <tr>\n          <td><strong>\uc0c1\uc218<\/strong><\/td>\n          <td>1 \u2194 1\/s<\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\uc9c0\uc218\ud568\uc218<\/strong><\/td>\n          <td>\n            e<sup>at<\/sup> \u2194 1\/(s-a)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\uac70\ub4ed\uc81c\uacf1<\/strong><\/td>\n          <td>\n            t<sup>n<\/sup> \u2194 n!\/s<sup>n+1<\/sup>\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Frequency Shift<\/strong><\/td>\n          <td>\n            e<sup>at<\/sup>f(t) \u2194 F(s-a)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Time Delay<\/strong><\/td>\n          <td>\n            f(t-\u03bb) \u2194 e<sup>-s\u03bb<\/sup>F(s)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\ubbf8\ubd84<\/strong><\/td>\n          <td>\n            f'(t) \u2194 sF(s)-f(0)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>\uc801\ubd84<\/strong><\/td>\n          <td>\n            \u222bf(t)dt \u2194 F(s)\/s\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Sin<\/strong><\/td>\n          <td>\n            sin at \u2194 a\/(s\u00b2+a\u00b2)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Cos<\/strong><\/td>\n          <td>\n            cos at \u2194 s\/(s\u00b2+a\u00b2)\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Time Delay Phase<\/strong><\/td>\n          <td>\n            e<sup>-j\u03c9\u03bb<\/sup>\n            \u2192 |M|=1,\n            \u2220=-\u03c9\u03bb\n          <\/td>\n        <\/tr>\n\n      <\/tbody>\n\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>14. \ud575\uc2ec \uae30\uc5b5 \ubb38\uc7a5<\/h2>\n\n  <div class=\"memory\">\n\n    <ol>\n\n      <li>\n        <strong>\n          t<sup>n<\/sup>\uc758 Laplace Transform\uc740\n          n!\/s<sup>n+1<\/sup>\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          Gamma Function\uc740\n          \u0393(n+1)=n! \uad00\uacc4\ub97c \uac00\uc9c4\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \uc2dc\uac04\uc601\uc5ed\uc5d0\uc11c e<sup>at<\/sup>\ub97c \uacf1\ud558\uba74\n          s-domain\uc5d0\uc11c F(s-a)\uac00 \ub41c\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \uc2dc\uac04\uc9c0\uc5f0 f(t-\u03bb)\uc740\n          s-domain\uc5d0\uc11c e<sup>-s\u03bb<\/sup>F(s)\uac00 \ub41c\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \ubbf8\ubd84\uc740 s\uc758 \uacf1\uc148,\n          \uc801\ubd84\uc740 1\/s\uc758 \uacf1\uc148\uc73c\ub85c \ubcc0\ud658\ub41c\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \uc21c\uc218 \uc2dc\uac04\uc9c0\uc5f0 e<sup>-j\u03c9\u03bb<\/sup>\uc758 \ud06c\uae30\ub294 1\uc774\uace0\n          \uc704\uc0c1\uc740 -\u03c9\u03bb\uc774\ub2e4.\n        <\/strong>\n      <\/li>\n\n      <li>\n        <strong>\n          \ub530\ub77c\uc11c \uc2dc\uac04\uc9c0\uc5f0\uc740 gain\uc744 \ubcc0\ud654\uc2dc\ud0a4\uc9c0 \uc54a\uc9c0\ub9cc\n          Phase Margin\uc744 \uac10\uc18c\uc2dc\ud0ac \uc218 \uc788\ub2e4.\n        <\/strong>\n      <\/li>\n\n    <\/ol>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"keywords\">\n    Laplace Transform, Gamma Function, t^n,\n    Frequency Shift, Time Delay, Derivative,\n    Integral, sin, cos, Phase Delay, Phase Margin\n  <\/div>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/byjusexamprep.com\/gate-eee\/laplace-transform#toc-2 Definition: The gamma function of n, written \u0393(n), is \u222b 0\u221e e-xxn-1dx. Recursively \u0393(n+1) = n\u0393(n). For non-negative integers \u0393(n+1) = n!. &#8220;`html Laplace Transform 2 Laplace Transform Table \u00b7 Gamma Function \u00b7 Frequency Shift \u00b7 Time Delay \u00b7 \ubbf8\ubd84 \u00b7 \uc801\ubd84 1. \uae30\ubcf8 Laplace Transform Table f(t) \u2112{f(t)} 1 1\/s eat 1\/(s-a) tn [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1185],"tags":[1192,1208,1209],"class_list":["post-6060","post","type-post","status-publish","format-standard","hentry","category-1185","tag-laplace-transform","tag-1208","tag-1209"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6060","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/comments?post=6060"}],"version-history":[{"count":3,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6060\/revisions"}],"predecessor-version":[{"id":9543,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6060\/revisions\/9543"}],"wp:attachment":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/media?parent=6060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/categories?post=6060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/tags?post=6060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}