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In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value a_{o} at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be  

  • Option 1)

    \frac{a_{0}}{}2

  • Option 2)

    \frac{a_{0}}{}4

  • Option 3)

    \frac{a_{0}}{}6

  • Option 4)

    \frac{a_{0}}{}9

 

Answers (1)

best_answer

In damped oscillation, amplitude goes on decaying exponentially 
where b = damping coefficient
Intially, \frac{a_{0}}{3} = a_{o}e^{-b\times 100T}T = time of one oscillation

or \frac{1}{3} = e^{-100bT}
Finally , a = a_{o}e^{-b\times 200T} or a = a_{o}(e^{-b\times 100T})^{2}

or a = a_{o}(\frac{1}{3})^{2}

or  a = a_{o}(\frac{a_{o}}{9})

 

Resultant amplitude in damped oscillation -

A=A_{0}.e^{-\frac{bt}{2m}}

E=E_{0}.e^{-\frac{bt}{2m}}

- wherein

A= Amplitude

E= Energy

 

 

 


Option 1)

\frac{a_{0}}{}2

This is incorrect.

Option 2)

\frac{a_{0}}{}4

This is incorrect.

Option 3)

\frac{a_{0}}{}6

This is incorrect.

Option 4)

\frac{a_{0}}{}9

This is correct.

Posted by

divya.saini

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