Question

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: $\frac{\text { major axis (along } X \text { ) }}{\text { minor axis (along } Y)}=20 \pi$ What is the frequency of the simple harmonic motion?

• A. 100 Hz
• B. 20 Hz
• C. 10 Hz
• D. $\frac{1}{10} Hz$

Answer 1

Answer: (C)

10 Hz

Answer 2

In representation of simple harmonic motion in ellipse as velocity along $X$ -axis and displacement along $Y$ -axis.
$\because \frac{\text { Major axis (along } X \text { -axis) }}{\text { Minor axis (along } X \text { -axis) }}=20 \pi$
$\Rightarrow \frac{\omega A}{A}=20 \pi$
$\Rightarrow \omega=20 \pi$
$\Rightarrow 2 \pi n=20 \pi$
The frequency of the simple harmonic motion
$\therefore\, n=10\, Hz$