Question

The total vibrational energy of a particle in S.H.M. is $E$. Its kinetic energy at half the amplitude from mean position will be :

• A. $\frac{E}{2}$
• B. $\frac{E}{3}$
• C. $\frac{E}{4}$
• D. $\frac{3E}{4}$

Answer 1

The correct option is D $\frac{3E}{4}$

The total vibrational energy of a particle in S.H.M is given by,

$E=\frac{1}{2}m{\omega }^2{a}^2$. . . . .(1)

The kinetic energy ,

$K.E=\frac{1}{2}m{\omega }^2(a^2-x^2)$

At $x=\frac{a}{2}$

$K.E=\frac{1}{2}m{\omega }^2(a^2-\frac{a^2}{4})$

$K.E=\frac{3}{4}\frac{1}{2}m{\omega }^2{a}^2$

$K.E=\frac{3}{4}E$ (from equation 1)

The correct option is D.