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Mechanical Properties Of Fluids

Question
CBSEENPH11020626
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Out of the following functions representing motion of a particle which represents SHM

space straight I space. space straight y space equals space sin space ωt space minus space cos space ωt II. space straight y space equals space sin squared space ωt III. space straight y space equals space 5 space cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction minus space 3 space ωt close parentheses IV. space straight y space equals space 1 space plus space ωt space plus space straight omega squared straight t squared

  • Only (IV) does not represent SHM

  • (I) and (III)

  • (I) and (II)

  • Only (I)

Solution

C.

(I) and (II)

For a simple harmonic motion

fraction numerator straight d squared straight y over denominator dt squared end fraction space proportional to space minus space straight y Hence comma space equation space straight y space equals space sin space ωt space minus space cos space ωt space and space straight y space equals space 5 space cos space open parentheses fraction numerator 3 straight pi over denominator 4 end fraction space minus space 3 ωt close parentheses space are space satisfying space this condition space and space equation space straight y space equals space 1 space plus space ωt space plus space straight omega squared straight t squared space is space not periodic space and space straight y space equals space sin cubed space ωt space is space periodic space but space not space SHM

Some More Questions From Mechanical Properties of Fluids Chapter

In the displacement equation y = r sin(ωt/ + ϕ) what does ϕ called and what information does it give?

What determines the natural frequency of an oscillator?

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?

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