Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • A Particle executes simple harmonic motion represented by displacement function as <img alt="x(t)=A \sin (\omega t+\phi )" src="https://entrancecorner.oncodecogs.com/gif.latex?x%28t%29%3DA%20%5Csin

A Particle executes simple harmonic motion represented by displacement function as x(t)=A \sin (\omega t+\phi ) In the Position and velocity of the Particle at  t=0  are  6 cm and  9 cm/s respectively then its amplitude is  A  find the value of  A

 

Option: 1

A=\frac{6}{sin\left [tan^{-1}\left ( \frac{2}{3} \right ) \right ]}


Option: 2

A=\frac{5}{sin\left [tan^{-1}\left ( \frac{2}{3} \right ) \right ]}


Option: 3

A=\frac{8}{sin\left [tan^{-1}\left ( \frac{2}{3} \right ) \right ]}


Option: 4

A=\frac{3}{sin\left [tan^{-1}\left ( \frac{2}{3} \right ) \right ]}


Answers (1)

best_answer

x=A \sin (\omega t+\varphi) \\

V=A \omega \cos (\omega t+\varphi) \\

t=0, \quad 6 =A\, \sin \varphi \quad\rightarrow \text { eq (1) } \\

\quad 9 \,\omega=A\, \omega \cos \varphi \quad

\quad 9 =A\, \cos \varphi \quad \rightarrow \text { eq (2) }

dividing by eq (1) and (2)

\frac{6}{9}=\frac{A \sin \varphi}{A \cos \varphi} \\

\frac{2}{3}=\tan \varphi \\
\varphi=\tan ^{-1}\left(\frac{2}{3}\right)

Put the value of eq (1)

6=A \sin \left[\tan ^{-1}\left(\frac{2}{3}\right)\right] \\

A=\frac{6}{sin\left [tan^{-1}\left ( \frac{2}{3} \right ) \right ]}



 

Posted by

avinash.dongre

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

NEET Paper Leak: Court extends CBI custody of accused Manisha Hawaldar by 2 days
anam-khan

'PM Modi personally supervising the situation': Centre tells SC in NEET case
anam-khan

NEET Paper Leak Row: NTA informs SC of security overhaul, institutional reforms

Latest Question