Question

A particle is vibrating in a simple harmonic motion with an amplitude of $4 \,cm$. At what displacement from the equilibrium position, is its energy half potential and half kinetic?

• A. 1 cm
• B. $\sqrt 2 cm$
• C. 3 cm
• D. $2\sqrt 2 cm$

Answer 1

Answer: (D)

$2\sqrt 2 cm$

Answer 2

Let x be the point where KE = PE
$Hence \, \, \, \, \, \, \frac{1}{2}m \omega^2 (a^2 -x^2)=\frac{1}{2}m \omega^2 x^2$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 2x^2 =a^2, x=\frac{a}{\sqrt 2}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, x=\frac{4}{\sqrt 2}=2\sqrt 2 cm$