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Mechanical Properties Of Fluids

Question
CBSEENPH11020653
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A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be 

  • β2/α2

  • α/β

  • β2/α

  • 2πβ/α

Solution

D.

2πβ/α

For a particle executing SHM, we have maximum acceleration,
straight alpha space equals space Aω squared space.. space left parenthesis straight i right parenthesis Where space straight A space is space maximum space amplitude space and space straight omega space is space angular velocity space of space straight a space particle Maximum space velocity space straight beta space equals space Aω space space space space space.. left parenthesis ii right parenthesis Divideing space equ space left parenthesis straight i right parenthesis space by space equ. space left parenthesis ii right parenthesis space we space get straight alpha over straight beta space equals space Aω squared over Aω space rightwards double arrow space straight alpha over straight beta space equals space straight omega space equals space fraction numerator 2 straight pi over denominator straight T end fraction straight i. straight e. space comma space straight T space equals space fraction numerator 2 πβ over denominator straight alpha end fraction Thus comma space it space time space period space of space vibration comma space straight T space equals space fraction numerator 2 πβ over denominator straight alpha end fraction space

Some More Questions From Mechanical Properties of Fluids Chapter

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Define frequency.

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What is periodic motion?

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

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