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  • Can someone help me with this, - Oscillations and Waves - JEE Main-4

The motion of a particle varies with time according to the relation y =a(\sin \omega t + \cos \omega t), then 

  • Option 1)

    The motion is oscillatary but not SHM

  • Option 2)

    The motion is SHM with amplitude a

  • Option 3)

    The motion is SHM with amplitude a\sqrt{2}

  • Option 4)

    The motion is SHM with amplitude 2a

 

Answers (1)

y = a(\cos\omega t + \sin\omega t) = a\sqrt{2}\left [\frac{1}{\sqrt{2}} \cos\omega t +\frac{1}{\sqrt{2}} \sin\omega t\right ] \\* \Rightarrow y = a\sqrt{2}\left [ \sin 45\degree \cos\omega t + \cos 45\degree \sin\omega t \right ] = a\sqrt{2} \sin (\omega t + 45\degree) \\* \Rightarrow Amplitude = a\sqrt{2}

 

Resultant Amplitude of Two SHM -

A= \sqrt{A{_{1}}^{2}+A{_{2}}^{2}+2A{_{1}}A_{2}.\cos \phi }

A_{1}and A_{2} are amplitude of two SHM's. \phi is phase difference.

 

- wherein

Both SHM's are along same direction and of same frequency.

 

 

 


Option 1)

The motion is oscillatary but not SHM

This is incorrect.

Option 2)

The motion is SHM with amplitude a

This is incorrect.

Option 3)

The motion is SHM with amplitude a\sqrt{2}

This is correct.

Option 4)

The motion is SHM with amplitude 2a

This is incorrect.

Posted by

subam

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