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

27457 Solutions
5929 Solvers

Last Solution submitted on Jul 07, 2022

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

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'?

Solution Comments

Solution 8635650

1 Comment

1 Comment

Jessa Juarez on 6 Jul 2022 at 0:01

I incorrectly grouped the variables in solving for y so my code was wrong. Be careful on using parentheses!

Solution 6931014

1 Comment

1 Comment

Josh Klueber on 21 Nov 2021

tricky

Solution 6385312

1 Comment

1 Comment

Isabella Stellitano on 14 Nov 2021

Good problem

Solution 5774283

2 Comments

2 Comments

Zihao Wang on 16 May 2021

Who can recognize that symbol is "e" ???

Yuanhao Zhu on 6 Aug 2021

Yeah same, had to zoom in and see

Solution 5430080

1 Comment

1 Comment

TIMOTHY PIERGIOVANNI on 22 Apr 2021

linearly spaced is a good hint

Solution 5024721

1 Comment

1 Comment

李君 on 9 Mar 2021

question is easy, but you need to use linspace(min,max,n) to generate a array.

Solution 4929714

4 Comments

4 Comments

Show 1 older comment

Tesfaye Girma on 26 Feb 2021

here is the solution i didn't know what is wrong i tried many times can you help me please

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

Dyuman Joshi on 26 Feb 2021

You are assuming the value of some variables which should not be the case.

Also, it's best to not post solutions (or solution attempts) in comments. Questions or comments specific to a solution can be posted in a comment tied to said solution or solution attempt.

decheng Lu on 13 Apr 2021

the solution is right. maybe this can be helpful.
t=1:T/(N-1):T;

Khoirul Anam on 12 Jul 2021

A and f must in solution

Solution 2955010

2 Comments

2 Comments

Snigdha Mallapragada on 16 Sep 2020

I couldn't identify what went wrong

Dyuman Joshi on 25 Feb 2021

Read the expression in the question again carefully

Solution 2630344

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

2 Comments

2 Comments

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.

Dyuman Joshi on 25 Feb 2021

Read the problem statement again carefully.

Problem Recent Solvers5929

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 Solvers5929

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 Solvers5929

Suggested Problems

More from this Author13

Problem Tags

Community Treasure Hunt

Players