# I SHM and the sign of k

#### Mr Davis 97

I have the equation for simple harmonic motion $\displaystyle \frac{d^2x}{dx^2} + k^2 x = 0$. I have a simple question. Do we need to make an assumption about the sign of $k$ before we solve this? We have that the roots satisfy $r^2=-k^2$. So $r=\pm i \sqrt{k^2}$. Do I need to assume $k$ is either positive or negative before I can proceed?

Related Differential Equations News on Phys.org

Homework Helper
Gold Member
2018 Award
Simple harmonic motion is what happens with a system that has a mass attached to a spring. The equation is $m \frac{d^2 x}{dt^2}=-kx$. The mass $m$ and spring constant $k$ are always both positive. The mass times acceleration is equal to the force which is opposite the displacement. $\\$ In the problem above $k^2>0$. The sign of $k$ doesn't matter. Most often, your $k$ is actually written as $\omega$.

#### Math_QED

Homework Helper
k is positive by definition, at least in this physics context.

"SHM and the sign of k"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving