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The displacement of a particle along the x-axis is given by x = a sin2\omegat. The motion of the particle corresponds to:

  • Option 1)

    simple harmonic motion of frequency \omega/\pi

  • Option 2)

    simple harmonic motion of frequency 3\omega/2\pi

  • Option 3)

    non simple harmonic motion

  • Option 4)

    simple harmonic motion of frequency \omega/2\pi

 

Answers (1)

best_answer

As we discussed

Composition of two SHM in perpendicular direction -

x=A_{1}sin omega t

y=A_{2}sin left ( omega t+delta 
ight )

 

 

- wherein

Resultant equation

frac{x^{2}}{A{_{1}}^{2}}+frac{y{_{2}}^{2}}{A{_{2}}^{2}}-frac{2xycos delta }{A_{1}A_{2}}= sin ^{2}delta

 

 x=a sin^2wt=\frac{a}{2}(1-cos2wt)

\frac{dx}{dt}=\frac{a}{2}200 \ Sin2wt

\frac{d^2x}{dt}=\frac{400^2a}{2} \ cos2wt

This represent as s.n.m of frequency = w/\pi


Option 1)

simple harmonic motion of frequency \omega/\pi

Correct

Option 2)

simple harmonic motion of frequency 3\omega/2\pi

Incorrect

Option 3)

non simple harmonic motion

Incorrect

Option 4)

simple harmonic motion of frequency \omega/2\pi

Incorrect

Posted by

divya.saini

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