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  • Can someone explain - Oscillations and Waves - JEE Main-3

The periodic time of the body executing simple harmonic motion is 3\; s. After how much interval from time t =0, its displacement will be half of its amplitude

  • Option 1)

    \frac{1}{8}\; s

  • Option 2)

    \frac{1}{6}\; s

  • Option 3)

    \frac{1}{4}\; s

  • Option 4)

    \frac{1}{3}\; s

 

Answers (1)

best_answer

\\*y = 2\sin\frac{2\pi}{T} t \Rightarrow \frac{a}{2} =a\sin\frac{2\pi t}{3} \Rightarrow \frac{1}{2} = sin\frac{2\pi t}{3} \\* \sin\frac{2\pi t}{3} = \sin\frac{\pi}{6} \Rightarrow \frac{2\pi t}{3} = \frac{\pi}{6} \Rightarrow t = \frac{1}{4} sec

 

Phase constant -

The constant \delta appearing in eqation x=A\sin \left ( wt+\delta \right ) is called phase constant. It describes initial state.

 

- wherein

This constant depends on the choice of the instant t=0.

 

 

 


Option 1)

\frac{1}{8}\; s

This is incorrect.

Option 2)

\frac{1}{6}\; s

This is incorrect.

Option 3)

\frac{1}{4}\; s

This is correct.

Option 4)

\frac{1}{3}\; s

This is incorrect.

Posted by

prateek

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