Question

The average energy in one time period in simple harmonic motion is.

• A. $\frac{1}{2}m{\omega }^2{A}^2$
• B. $\frac{1}{4}m{\omega }^2{A}^2$
• C. $m{\omega }^2{A}^2$
• D. Zero

Answer 1

The correct option is A $\frac{1}{2}m{\omega }^2{A}^2$

Average Energy means the total energy of the Simple Harmonic Motion in One Time Period.

Energy is the Scalar Quantity and not the vector quantity, thus it only depends upon the magnitude and not on the direction.

Therefore, It cannot be zero as in case of the velocity, displacement, etc. It will must be having some numerical terms.

Total energy of the Simple Harmonic Motion = Kinetic Energy + Potential energy.

$=\frac{1}{2}k(A^2-x^2)+\frac{1}{2}k{x}^2$

$=\frac{1}{2}k{A}^2-\frac{1}{2}k{x}^2+\frac{1}{2}k{x}^2$

$=\frac{1}{2}k{A}^2=\frac{1}{2}m{\omega }^2{A}^2$