# GATE Papers >> EEE >> 2019 >> Question No 38

Question No. 38

A periodic function $f(t)$, with a period of $2\pi$, is represented as its Fourier series,

$f(t)=a_0+{\textstyle\sum_{n=1}^\infty}\;a_n\;\cos nt\;+{\textstyle\sum_{n=1}^\infty}\;b_n\sin\;nt.$

If

$f(t)=\left\{\begin{array}{lc}A\;\sin\;t,&0\;\leq\;t\;\pi\\0,&\;\;\;\;\;\pi\;<\;t\;<\;2\pi\end{array},\right.$

the Fourier series coefficients $a_1$ and $b_1$ of $f(t)$ are

##### Answer : (D) $a_1=0;\;b_1=\frac A2$

Solution of Question No 38 of GATE 2019 EEE Paper

As per the given description of f(t), if we draw its waveform, if looks like

→ One way to obtain its C.T.T.S is by obtaining its odd and even part and then by obtaining their individual C.T.F.S and finally we can add them to get complete C.T.F.S of f(t). However in this case we can pick the correct option by eliminating others.

$\mathrm f(\mathrm t)={\mathrm f}_{\mathrm o}(\mathrm t)1+\mathrm{fe}(\mathrm t)=\left[\frac{\mathrm f(\mathrm t)-\mathrm f(-\mathrm t)}2\right]+\left[\frac{\mathrm f(\mathrm t)+\mathrm f(-\mathrm t)}2\right]$

${\mathrm f}_{\mathrm o}(\mathrm t)=\left[\frac{\mathrm A}2{\mathrm{sinω}}_{\mathrm o}\mathrm t\right]+\sum\limits_{\mathrm n=1}^{\mathrm N}{\mathrm a}_{\mathrm n}{\mathrm{cosω}}_{\mathrm o}\mathrm t$

From this ${\mathrm b}_1=\frac{\mathrm A}2,$  So only option D satisfy this.

L6jHuO https://writemyessayforme.web.fc2.com/

Posted on  13/12/2020 05:34:28  by  dobson
7JImp7 https://beeg.x.fc2.com/

Posted on  26/01/2021 13:40:53  by  markus
E9geXh https://xnxxx.web.fc2.com/ xnxx

Posted on  29/06/2021 09:58:29  by  Merziuziy
https://beeg.x.fc2.com/sitemap1.html https://beeg.x.fc2.com/sitemap2.html https://xnxxx.web.fc2.com/sitemap1.html https://xnxxx.web.fc2.com/sitemap2.html https://xvideoss.web.fc2.com/sitemap1.html https://xvideoss.web.fc2.com/sitemap2.html

Posted on  03/08/2021 14:31:00  by  johnanz

Posted on  04/12/2020 02:53:37  by  dobson
RY53Nq http://xnxx.in.net/ xnxx videos

Posted on  13/12/2020 00:14:47  by  johnan
kYuRK5 https://writemyessayforme.web.fc2.com/#writemyessay

Posted on  15/12/2020 06:34:08  by  dobson
d0Ej1m http://waldorfdollshop.us/ waldorf doll

Posted on  09/01/2021 13:05:58  by  johnanz
write my essays writemypaper.online

Posted on  22/07/2021 22:15:54  by  johnansog
https://xvideoss.web.fc2.com/

Posted on  03/08/2021 14:39:15  by  johnanz
Where do you study? http://tubereviews.online porntube EDI meets the test of fiduciary responsibility. "By disintermediating Wall Street, investors can invest again with more predictable returns," adds Fullerton. "Managers can manage the complex long term challenges of their multiple stakeholders, and the economy will be healthier as a result." Let's hope some fund managers see these advantages and give EDI a try.

Posted on  12/08/2021 01:24:56  by  Roger
Could you transfer $1000 from my current account to my deposit account? http://porntubereview.online apetube Residents of La Pintada, a remote village of about 600 people north-west of Acapulco, described how the hillside buried their homes as they were holding independence day celebrations on Monday evening. Posted on 12/08/2021 01:24:57 by Marcellus Have you seen any good films recently? http://porntuberating.online pornhub Republicans said they would also approve a bill repealing atax on medical devices that helps fund the healthcare law to thetune of about$30 billion. That provision, sought with heavylobbying by the medical device industry, has been supported inthe past by some Democratic senators.

Posted on  12/08/2021 01:24:57  by  Zachery
I'm happy very good site http://tuberating.online youjizz He suspects the NCAAâs punishment has something to do with the level of athletes that are coming Findlay Prep and Huntinton Prep. Findlay Prep produced the top pick in Juneâs draft and has won three of the past five ESPN National High School invitational championships, a prestigious tournament involving some of the top teams in the country. And Huntington Prep most recently produced Andrew Wiggins, widely considered the top freshman in college basketball and who has been compared to LeBron James and goes to Kansas.

Posted on  12/08/2021 01:24:58  by  Russel
I'm on a course at the moment http://porntuberating.online elephanttube The US House of Representatives passed a bill on Wednesday by a commanding 400-20 bipartisan majority to tighten sanctions on Iranâs petroleum sector. The move came just days before the inauguration of Rouhani on Sunday as Iranâs new president.

Posted on  12/08/2021 01:24:58  by  Stewart