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Can someone explain - Oscillations and Waves - JEE Main-5

The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of \pi results in the displacement of the particle along 

  • Option 1)

    Straight Line

  • Option 2)

    Circle

  • Option 3)

    Ellipse

  • Option 4)

    Figure of eight

 
Answers (1)
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If y_{1} = a_{1}\sin\omega t and y_{2} = a_{2}\sin(\omega t + \pi)

\Rightarrow \frac{y_{1}}{a_{1}} + \frac{y_{2}}{a_{2}} = 0 \Rightarrow y_{2} = -\frac{a_2}{a_{1}}y_{1}

This is 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)

Straight Line

This is correct.

Option 2)

Circle

This is incorrect.

Option 3)

Ellipse

This is incorrect.

Option 4)

Figure of eight

This is incorrect.

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