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  • Help me solve this Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose the resultant form of vibration will be

Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose the resultant form of vibration will be

  • Option 1)

    A circle

  • Option 2)

    An ellipse

  • Option 3)

    A straight line

  • Option 4)

    A parabola

 

Answers (1)

best_answer

If   y_{1} = a_{1}\sin\omega t andy_{2} = a_{2}\sin(\omega t + 0) = a_{2}\sin{\omega t}

\Rightarrow \frac{y_{1}^{2}}{a_{1}^{2}} + \frac{y_{2}^{2}}{a_{2}^{2}} - \frac{2y_{1}y_{2}}{a_{1}a_{2}} = \Rightarrow y_{2} = \frac{a_{2}}{a_{1}}y_{1}

This is a equation of straight line.

 

Resultant equation of two perpendicular SHM when δ = 0 -

Resultant equation

y= \frac{A_{2}}{A_{1}}.x

 

- wherein

It is a straight line with slope

\frac{A_{2}}{A_{1}}

 

 

 


Option 1)

A circle

This is incorrect.

Option 2)

An ellipse

This is incorrect.

Option 3)

A straight line

This is correct.

Option 4)

A parabola

This is incorrect.

Posted by

Aadil

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