Problem 44948. Calculate a Damped Sinusoid

Created by Pooja Lalan

Solve Later

{"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>"}]}

Solve

Solution Stats

14140 Solutions
2732 Solvers

Last Solution submitted on Jan 18, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Arif Caliskan on 5 Mar 2020

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

Shuang Hu on 5 Oct 2020

t=linspace(0,T,N);
y=exp(-lambda*t).*cos(2*pi*t);

Solution Comments

Solution 2955010

1 Comment

1 Comment

Snigdha Mallapragada on 16 Sep 2020

I couldn't identify what went wrong

Solution 2630344

1 Comment

1 Comment

Umur Ulas Harman on 29 Jun 2020

function y = damped_cos(lambda, T, N)
A=1;
f=1;
t=linspace(0,T,N);

y = A*exp(-lambda*t).*cos(2*pi*f*t);
end

Solution 2285385

3 Comments

3 Comments

silki baghla on 16 May 2020

I am not getting the error in my code.Though,its working in MATLAB script.please help

silki baghla on 18 May 2020

Anyone who has solved the problem, please help.I have developed the code according to the details and it's working well in matlab. I dont know why it is incorrect here.

Prathmesh Vhatkar on 29 May 2020

Did you check the online and offline MATLAB's version?

Solution 2253914

1 Comment

1 Comment

TARUN PRATAP SINGH on 4 May 2020

I didn't understand why my code not working here,it worked on my Matlab but not here.

Problem Recent Solvers2732

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44948. Calculate a Damped Sinusoid

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2732

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Problem 44948. Calculate a Damped Sinusoid

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2732

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players