Question

The velocity of a particle executing a simple harmonic motion is $13\, ms^{-1}$, when its distance from the equilibrium position (Q) is 3 m and its velocity is $12 \, ms^{-1}$, when it is 5 m away from The frequency of the simple harmonic motion is

• A. $\frac{5\pi}{8}$
• B. $\frac{5}{8\pi}$
• C. $\frac{8\pi}{5}$
• D. $\frac{8}{5\pi}$

Answer 1

Answer: (B)

$\frac{5}{8\pi}$

Answer 2

Using $v = \omega\sqrt{A^{2}-x^{2}}, 13^{2} = \omega^{2} \left(A^{2}-3^{2}\right), 12^{2} = \omega^{2} \left(A^{2}-5^{2}\right)$
$\Rightarrow \omega = \frac{5}{8\pi}$