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# Engineering

The displacement of a damped harmonic oscillator is given by 

x(t)=e^{-0.1t}cos(10\pi t +\phi )

Here t is in seconds. The time taken for its apmlitude of vibration

to drop to half of its initial value is close to:

  • Option 1)

    4\: s

  • Option 2)

    7\: s

  • Option 3)

    13\: s

  • Option 4)

    27\: s

 

Answers (1)
S solutionqc

 

Resultant amplitude in damped oscillation -

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

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

- wherein

A= Amplitude

E= Energy

 

 

x(t)=e^{-0.1t}cos(10\pi t +\phi )

amplitude changes from A_o\: \: to\: \: \frac{A_o}{2}

=> \frac{A_o}{2}=A_oe^{-0.1t}

\ln 2=0.1t

t=\frac{\ln 2}{0.1}=\frac{0.7}{0.1}\approx 7sec


Option 1)

4\: s

Option 2)

7\: s

Option 3)

13\: s

Option 4)

27\: s

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