Q65 / 90 · JEE Main 2009 · Physics

If $x, v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $\mathrm{T}$, then, which of the following does not change with time?

  • A
    $a^2 T^2+4 \pi^2 v^2$
  • Correct answer
    B
    $\frac{a T}{x}$
  • C
    $a T+2 \pi v$
  • D
    $\frac{a T}{v}$

Solution

$$ \frac{\text { aT }}{\mathrm{X}}=\frac{\omega^2 \mathrm{XT}}{\mathrm{X}}=\frac{4 \pi^2}{\mathrm{~T}^2} \times \mathrm{T}=\frac{4 \pi^2}{\mathrm{~T}}=\text { constant. } $$

Hence, the correct answer is option: 'B'.

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