In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

Question

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. (A) (1/2) (B) (3/4) (C) (1/3) (D) (1/4)

Tardigrade Admin · Accepted Answer

K=(1/2) m ω2(A2-x2) =(1/2) m ω2(A2-(A2/4)) =(1/2) m ω2((3 A2/4)) K=(3/4)((1/2) m ω2 A2)

Q. In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{1}{3}$

$\frac{1}{4}$

$K = \frac{1}{2} m ω^{2} (A^{2} - x^{2})$
$= \frac{1}{2} m ω^{2} (A^{2} - \frac{A ^{2}}{4})$
$= \frac{1}{2} m ω^{2} (\frac{3 A ^{2}}{4})$
$K = \frac{3}{4} (\frac{1}{2} m ω^{2} A^{2})$