Question

Which of the following is correct about SHM along a straight line ?

• A. Ratio of acceleration to velocity is constant
• B. Ratio of acceleration to potential energy is constant
• C. Ratio of acceleration to displacement from the mean position is constant
• D. Ratio of acceleration to kinetic energy is constant

Answer 1

The correct option is C Ratio of acceleration to displacement from the mean position is constant

$V=\pm \omega \sqrt{A^2-x^2},PE=\frac{1}{2}k{x}^{2}a=-{\omega }^{2}xKE=\frac{1}{2}m{\omega }^2(A^2-x^2)=\frac{1}{2}k(A^2-x^2)$

Ratio of acceleration to displacement $=\frac{-{\omega }^{2}x}{x}=-{\omega }^2$ (constant)