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  • How to solve this problem- - Oscillations and Waves - BITSAT

If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = Os \: to \: t =\tau sThen \tau may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

  • Option 1)

    \frac{0.693}{b}

  • Option 2)

    b

  • Option 3)

    \frac{1}{b}

  • Option 4)

    \frac{2}{b}

 

Answers (1)

best_answer

As we learned 

 

Resultant amplitude in damped oscillation -

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

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

- wherein

A= Amplitude

E= Energy

 

 The amplitude of damped oscillator is \theta =\theta _{0}\theta =\theta _{0}\; e^{\frac{-ht}{2}}

\Rightarrow \therefore at\; t=T,\theta =\frac{\theta _{0}}{e}

\Rightarrow \frac{\theta _{0}}{e}=\theta _{0}.e^{\frac{-bt}{2}}\; or\; \frac{bt}{2}=1

or\; t=\frac{2}{b}

 


Option 1)

\frac{0.693}{b}

Option 2)

b

Option 3)

\frac{1}{b}

Option 4)

\frac{2}{b}

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Aadil

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