Q127 / 155 · WBJEE 2018 · Physics

In case of a simple harmonic motion, if the velocity is plotted along the $X$ -axis and the displacement (from the equilibrium position) is plotted along the $Y$ -axis, the resultant curve happens to be an ellipse with the ratio: major axis (along X) $=20 \pi$ minor axis (along $Y)$ What is the frequency of the simple harmonic motion?

  • A
    $100 \mathrm{Hz}$
  • B
    $20 \mathrm{Hz}$
  • Correct answer
    C
    $10 \mathrm{Hz}$
  • D
    $\frac{1}{10} \mathrm{Hz}$

Solution

In representation of simple harmonic motion in ellipse as velocity along $X$ -axis and displacement along $Y$ -axis. $\frac{\text { Major axis (along } X \text { -axis) }}{\text { Minor axis (along } X \text { -axis) }}=20 \pi$ $\Rightarrow \quad \frac{\omega A}{A}=20 \pi \Rightarrow \omega=20 \pi$ The frequency of the simple harmonic motion

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

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