A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s-1) is :

  • Option 1)

    \frac{1}{30}ln 3

  • Option 2)

    \frac{1}{15}ln 3

  • Option 3)

    2

  • Option 4)

    \frac{1}{2}

 

Answers (1)

As we learnt in  

Resultant amplitude in damped oscillation -

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

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

- wherein

A= Amplitude

E= Energy

 

 As we know that E=E_{0}e^{-bt/m}

    15=45e^{-156/m}\ \; \Rightarrow\ \; \frac{1}{3}=e^{-156/3}

Taking log both side

    \frac{b}{m}=\frac{1}{15}ln3

Correct option is 2.

 

 


Option 1)

\frac{1}{30}ln 3

This is an incorrect option.

Option 2)

\frac{1}{15}ln 3

This is the corrct option.

Option 3)

2

This is an incorrect option.

Option 4)

\frac{1}{2}

This is an incorrect option.

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