Laplace Transform Inverse Problem - 1

Finding <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="0" style="font-size: 113.1%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c210E TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D461 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container> from Transfer Function <mjx-container class="MathJax CtxtMenu_Attached_0" jax="CHTML" tabindex="0" ctxtmenu_counter="1" style="font-size: 113.1%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43B TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml></mjx-container>

Find h(t) from H(s)=s2s3+4s2+4s

Answer:

h(t)=e−2t−2te−2t

Discussion

Graph:h(t)=e−2t−2te−2t
 [05220240605]

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