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:
$\frac{majoraxis\left(alongX\right)}{minoraxis\left(alongY\right)}=20\pi$
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

Relation between velocity & x is SHM in H.
$\frac{v^2}{{\omega }^2{A}^2}+\frac{x^2}{A^2}=1$ $\to$ Ellipse
Major axis $=2\Omega A$
Minor axis $=2a$
Given: $\frac{2\Omega a}{2a}$
$\Omega =20\pi$
$2\pi f=20\pi$
$f=10$Hz.