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    <title>MaplePrimes - answers and comments on Question, Inverse laplace with variable coefficient</title>
    <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient</link>
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    <lastBuildDate>Sun, 14 Jun 2026 02:33:03 GMT</lastBuildDate>
    <pubDate>Sun, 14 Jun 2026 02:33:03 GMT</pubDate>
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    <description>The latest answers and comments added to the Question, Inverse laplace with variable coefficient</description>
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      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - answers and comments on Question, Inverse laplace with variable coefficient</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient</link>
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    <item>
      <title>By assume</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient?ref=Feed:MaplePrimes:Inverse laplace with variable coefficient:Comments#answer142984</link>
      <itunes:summary>&lt;p&gt;How about this?&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/534e318293e0ecfc68fa54f27bfd8d45.gif" alt="assume(zeta &amp;lt; 1):" width="285" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/e26c620e7efaa9cb7a7695576e15f1f0.gif" alt="Step_Respon := 1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="448" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -43;" src="/view.aspx?sf=142984/452948/823719112c994ab684a9171b01ba9c7b.gif" alt="1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="224" height="69"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/c9271a3af92cc286206bcd69ee2335c1.gif" alt="with(inttrans); -1; invlaplace(Step_Respon, s, x)" width="281" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -65;" src="/view.aspx?sf=142984/452948/6b2e037ba864fdeb27a85b4ca6d1687c.gif" alt="1-cos((-zeta^2+1)^(1/2)*omega_n*x)*exp(-x*zeta*omega_n)-zeta*sin((-zeta^2+1)^(1/2)*omega_n*x)*exp(-x*zeta*omega_n)/(-zeta^2+1)^(1/2)" width="546" height="92" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
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&lt;/tbody&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/b079b80ac2fe070abd189edbdd4cb46c.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=142984/452948/assume.mw"&gt;Download assume.mw&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;Compare with&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/f9078b38946b1ce89a16c963e639753b.gif" alt="restart; Step_Respon := 1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="508" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/045d49f85dfa39cc9a7846cb27cad59a.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/d19fe12d2124c7a9f40231dbd9f1bc02.gif" alt="with(inttrans); -1; `assuming`([invlaplace(Step_Respon, s, x)], [zeta &amp;lt; 1])" width="391" height="23"&gt;&lt;/p&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -77;" src="/view.aspx?sf=142984/452948/96dbe7e2e8536c26de0bb23b70587f9f.gif" alt="1-cosh(((zeta^2-1)*omega_n^2)^(1/2)*x)*exp(-x*zeta*omega_n)+((zeta+1)*omega_n^2/(zeta-1))^(1/2)*sinh(((zeta^2-1)*omega_n^2)^(1/2)*x)*exp(-x*zeta*omega_n)*zeta/((zeta+1)*omega_n)" width="546" height="104" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
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&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/419253b726e4e04dc5aaebf09a865ebf.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;</itunes:summary>
      <description>&lt;p&gt;How about this?&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/534e318293e0ecfc68fa54f27bfd8d45.gif" alt="assume(zeta &amp;lt; 1):" width="285" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/e26c620e7efaa9cb7a7695576e15f1f0.gif" alt="Step_Respon := 1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="448" height="23"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -43;" src="/view.aspx?sf=142984/452948/823719112c994ab684a9171b01ba9c7b.gif" alt="1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="224" height="69"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/c9271a3af92cc286206bcd69ee2335c1.gif" alt="with(inttrans); -1; invlaplace(Step_Respon, s, x)" width="281" height="23"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -65;" src="/view.aspx?sf=142984/452948/6b2e037ba864fdeb27a85b4ca6d1687c.gif" alt="1-cos((-zeta^2+1)^(1/2)*omega_n*x)*exp(-x*zeta*omega_n)-zeta*sin((-zeta^2+1)^(1/2)*omega_n*x)*exp(-x*zeta*omega_n)/(-zeta^2+1)^(1/2)" width="546" height="92" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(2)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/b079b80ac2fe070abd189edbdd4cb46c.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=142984/452948/assume.mw"&gt;Download assume.mw&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;Compare with&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;form name="worksheet_form"&gt;
&lt;table style="width: 576px;" align="center"&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/f9078b38946b1ce89a16c963e639753b.gif" alt="restart; Step_Respon := 1/(s*(s^2/omega_n^2+2*zeta*s/omega_n+1))" width="508" height="23"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/045d49f85dfa39cc9a7846cb27cad59a.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/d19fe12d2124c7a9f40231dbd9f1bc02.gif" alt="with(inttrans); -1; `assuming`([invlaplace(Step_Respon, s, x)], [zeta &amp;lt; 1])" width="391" height="23"&gt;&lt;/p&gt;
&lt;table&gt;
&lt;tbody&gt;
&lt;tr valign="baseline"&gt;
&lt;td&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"&gt;&lt;img style="vertical-align: -77;" src="/view.aspx?sf=142984/452948/96dbe7e2e8536c26de0bb23b70587f9f.gif" alt="1-cosh(((zeta^2-1)*omega_n^2)^(1/2)*x)*exp(-x*zeta*omega_n)+((zeta+1)*omega_n^2/(zeta-1))^(1/2)*sinh(((zeta^2-1)*omega_n^2)^(1/2)*x)*exp(-x*zeta*omega_n)*zeta/((zeta+1)*omega_n)" width="546" height="104" align="middle"&gt;&lt;/p&gt;
&lt;/td&gt;
&lt;td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"&gt;(1)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"&gt;&lt;img style="vertical-align: -6;" src="/view.aspx?sf=142984/452948/419253b726e4e04dc5aaebf09a865ebf.gif" alt="``" width="11" height="23"&gt;&lt;/p&gt;
&lt;/td&gt;
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&lt;input type="hidden" name="sequence" value="1"&gt; &lt;input type="hidden" name="cmd" value="none"&gt;&lt;/form&gt;</description>
      <guid>142984</guid>
      <pubDate>Sun, 03 Feb 2013 00:18:32 Z</pubDate>
      <itunes:author>Markiyan Hirnyk</itunes:author>
      <author>Markiyan Hirnyk</author>
    </item>
    <item>
      <title>wow!!!
it works perfect, Markiyan, I got</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient?ref=Feed:MaplePrimes:Inverse laplace with variable coefficient:Comments#comment143000</link>
      <itunes:summary>&lt;p&gt;wow!!!&lt;/p&gt;
&lt;p&gt;it works perfect, Markiyan, I got exactly what I want, you are such a genious!!!&lt;/p&gt;
&lt;p&gt;I stuck with this problem for a long time!!! At first I got those ugly "sinh" &amp;amp; "cosh" expression without contraint on zeta:(&lt;/p&gt;
&lt;p&gt;PS: I'm a newbee in maple, is is possible for you to recommend some material on how to system learn maple?&lt;/p&gt;
&lt;p&gt;I really appreciate your help.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Best,&lt;/p&gt;
&lt;p&gt;Allan&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;wow!!!&lt;/p&gt;
&lt;p&gt;it works perfect, Markiyan, I got exactly what I want, you are such a genious!!!&lt;/p&gt;
&lt;p&gt;I stuck with this problem for a long time!!! At first I got those ugly "sinh" &amp;amp; "cosh" expression without contraint on zeta:(&lt;/p&gt;
&lt;p&gt;PS: I'm a newbee in maple, is is possible for you to recommend some material on how to system learn maple?&lt;/p&gt;
&lt;p&gt;I really appreciate your help.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Best,&lt;/p&gt;
&lt;p&gt;Allan&lt;/p&gt;</description>
      <guid>143000</guid>
      <pubDate>Sun, 03 Feb 2013 03:26:02 Z</pubDate>
      <itunes:author>roserope</itunes:author>
      <author>roserope</author>
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    <item>
      <title>Goldy,</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient?ref=Feed:MaplePrimes:Inverse laplace with variable coefficient:Comments#comment143001</link>
      <itunes:summary>&lt;p&gt;all pleasure is mine. Reading of Maple help is very useful.&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;all pleasure is mine. Reading of Maple help is very useful.&lt;/p&gt;</description>
      <guid>143001</guid>
      <pubDate>Sun, 03 Feb 2013 03:31:00 Z</pubDate>
      <itunes:author>Markiyan Hirnyk</itunes:author>
      <author>Markiyan Hirnyk</author>
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    <item>
      <title>Thanks!</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient?ref=Feed:MaplePrimes:Inverse laplace with variable coefficient:Comments#comment143007</link>
      <itunes:summary>&lt;p&gt;Thanks so much, Markiyan!&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;Thanks so much, Markiyan!&lt;/p&gt;</description>
      <guid>143007</guid>
      <pubDate>Sun, 03 Feb 2013 09:22:02 Z</pubDate>
      <itunes:author>roserope</itunes:author>
      <author>roserope</author>
    </item>
    <item>
      <title>Reading up on Maple</title>
      <link>http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient?ref=Feed:MaplePrimes:Inverse laplace with variable coefficient:Comments#comment143035</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient#comment143000"&gt;@roserope&lt;/a&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;As for reading material on Maple, there is quite a bit on the Web. A number of these are from University classes. One I downloaded and used is Problem Solving with Maple, by Carl Eberhart, carl@ms.uky.edu from U. of Kentucky. There are others as well. Google is your friend. Also depends a little on what you need (e.g. calculus vs linear algebra).&lt;/p&gt;
&lt;p&gt;A number of these are relatively old and use earlier Maple versions all the way back to Maple V. But do not let this discourage you; the basics have not changed that much. The Maple docs (User guide and Programming guide &amp;amp; whatever else there is) are actually useful as well and available online at Maplesoft.com.&lt;/p&gt;
&lt;p&gt;You do want to peruse the Help facility often. While not perfect there is a lot of good info in there.&lt;/p&gt;
&lt;p&gt;Finally, start with simpler problems even if you can do them faster by hand. In that way you'll get the hang of Maple &amp;amp; its idiosyncrasies. For more complicated problems it almost always pays off to break them down into steps &amp;amp; guide Maple along. Maple won't solve a biggie for you in one command (at least not usually). But if you take it through the steps it may well get to the solution and avoid tripping up on details as we humans are often prone to do.&lt;/p&gt;
&lt;p&gt;Maple is a sophisticated tool that comes with a learning curve so you'll need to invest some time. If you work or will want to work in a technical/scientific field, this investment will pay off big time, though.&lt;/p&gt;
&lt;p&gt;Mac Dude&lt;/p&gt;</itunes:summary>
      <description>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/questions/142980-Inverse-Laplace-With-Variable-Coefficient#comment143000"&gt;@roserope&lt;/a&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;As for reading material on Maple, there is quite a bit on the Web. A number of these are from University classes. One I downloaded and used is Problem Solving with Maple, by Carl Eberhart, carl@ms.uky.edu from U. of Kentucky. There are others as well. Google is your friend. Also depends a little on what you need (e.g. calculus vs linear algebra).&lt;/p&gt;
&lt;p&gt;A number of these are relatively old and use earlier Maple versions all the way back to Maple V. But do not let this discourage you; the basics have not changed that much. The Maple docs (User guide and Programming guide &amp;amp; whatever else there is) are actually useful as well and available online at Maplesoft.com.&lt;/p&gt;
&lt;p&gt;You do want to peruse the Help facility often. While not perfect there is a lot of good info in there.&lt;/p&gt;
&lt;p&gt;Finally, start with simpler problems even if you can do them faster by hand. In that way you'll get the hang of Maple &amp;amp; its idiosyncrasies. For more complicated problems it almost always pays off to break them down into steps &amp;amp; guide Maple along. Maple won't solve a biggie for you in one command (at least not usually). But if you take it through the steps it may well get to the solution and avoid tripping up on details as we humans are often prone to do.&lt;/p&gt;
&lt;p&gt;Maple is a sophisticated tool that comes with a learning curve so you'll need to invest some time. If you work or will want to work in a technical/scientific field, this investment will pay off big time, though.&lt;/p&gt;
&lt;p&gt;Mac Dude&lt;/p&gt;</description>
      <guid>143035</guid>
      <pubDate>Mon, 04 Feb 2013 01:50:07 Z</pubDate>
      <itunes:author>Mac Dude</itunes:author>
      <author>Mac Dude</author>
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