First slide

Simple hormonic motion

Question

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

Moderate

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.

Solution

V = $\pm ω \sqrt{A^{2} - x^{2}}, PE = \frac{1}{2} {kx}^{2}$
$a = - ω^{2} x$
KE = $\frac{1}{2} m ω^{2} (A^{2} - x^{2}) = \frac{1}{2} k (A^{2} - x^{2})$
Ratio of acceleration to displacement = $\frac{- ω^{2} x}{x} = - ω^{2}$ (constant)

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