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  • Can someone help me with this, - Oscillations and Waves - JEE Main-3

The equation of motion of a particle is \frac{d^{2}y}{dt^{2}} + ky =0, where k is positve constant. The time period of the motion is given by

  • Option 1)

    \frac{2\pi}{k}

  • Option 2)

    2\pi k

  • Option 3)

    \frac{2\pi}{\sqrt{k}}

  • Option 4)

    2\pi\sqrt{k}

 

Answers (1)

best_answer

On camparing with standard equation  \frac{d^{2}y}{dt^{2}} + \omega^{2}y =0

we get \omega^{2} = k \Rightarrow \omega = \frac{2\pi}{T} = \sqrt{k} \Rightarrow T= \frac{2\pi}{\sqrt{k}}

 

Equation of S.H.M. -

a=-\frac{d^{2}x}{dt^{2}}= -w^{2}x

w= \sqrt{\frac{k}{m}}

 

- wherein

x= A\sin \left ( wt+\delta \right )

 

 

 


Option 1)

\frac{2\pi}{k}

This is incorrect.

Option 2)

2\pi k

This is incorrect.

Option 3)

\frac{2\pi}{\sqrt{k}}

This is correct.

Option 4)

2\pi\sqrt{k}

This is incorrect.

Posted by

prateek

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