Problem 44948. Calculate a Damped Sinusoid

Created by Pooja Lalan

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The equation of a damped sinusoid can be written as</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>y = A.ⅇ^(-λt)*cos(2πft)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>A</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>λ</w:t></w:r><w:r><w:t>, and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>f</w:t></w:r><w:r><w:t> are scalars and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>t</w:t></w:r><w:r><w:t> is a vector.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Calculate the output sinusoid</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>y</w:t></w:r><w:r><w:t> given the inputs below:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>lambda -</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>λ</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>T</w:t></w:r><w:r><w:t> - maximum value of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>t</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> - number of elements in</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>t</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Assume</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>A = 1</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>f = 1</w:t></w:r><w:r><w:t> . The vector</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>t</w:t></w:r><w:r><w:t> should be linearly spaced from 0 to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>T</w:t></w:r><w:r><w:t>, with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> elements.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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Last Solution submitted on Sep 28, 2023

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Arif Caliskan on 5 Mar 2020

How can I find the solution I already failed to solve 15 times.

Yash Paranjape on 30 Dec 2021

Try reading the question again carefully and make sure you understand the linearly spaced part. It's a tricky one.

Siddharth Pachpor on 1 May 2022

I think i need explanation for this concept :
The vector t should be linearly spaced from 0 to T, with N elements.
if I do, a = 1:6, the ans is 1 2 3 4 5 6
but now if i do, a = 1:2:6, ans is 1 3 5
so for linear distributed vector to reach end point 6, we need to do,
a = 1:(6-1)/(6+1):6 --------similarly can it be done as t = 0:(T-1)/(T+1):T? what is the concept in the words 'linearly spaced'?

Seokbeom Chun on 7 Sep 2023 at 8:44

From the equation y = A.ⅇ^(-λt)*cos(2πft), it might be confused if you don't know the character between A and -λt is the 'euler number'.

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Problem 44948. Calculate a Damped Sinusoid

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