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Mechanical Properties Of Fluids

Question
CBSEENPH11020288
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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to α times its original magnitude, where α equals

  • 0.7

  • 0.81

  • 0.729

  • 0.6

Solution

C.

0.729

Amplitude of damped oscillator
straight A space equals space straight A subscript 0 straight e to the power of negative fraction numerator bt over denominator 2 straight m end fraction end exponent After space 5 straight s comma space space space 0.9 space straight A subscript straight o space equals space straight A subscript straight o straight e to the power of negative fraction numerator straight b left parenthesis 5 right parenthesis over denominator 2 straight m end fraction end exponent space space.. space left parenthesis straight i right parenthesis space After space 10 space more space second comma straight A space equals space straight A subscript straight o straight e to the power of negative straight b fraction numerator 15 over denominator 2 straight m end fraction end exponent straight A space equals space straight A subscript straight o open parentheses straight e to the power of negative straight b fraction numerator 15 over denominator 2 straight m end fraction end exponent close parentheses cubed space space... space left parenthesis ii right parenthesis From space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma straight A space equals space 0.729 space straight A subscript straight o space equals space αA subscript 0 Hence comma space straight alpha space equals space 0.729

Some More Questions From Mechanical Properties of Fluids Chapter

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Does the time period of particle vibrating in simple harmonic motion depend upon its displacement?

Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?

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