# SHM: Do We Need to Assume Sign of k?

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• Mr Davis 97
In summary, the conversation is about simple harmonic motion and the equation ##\displaystyle \frac{d^2x}{dx^2} + k^2 x = 0##. The question is whether an assumption needs to be made about the sign of ##k## before solving. The answer is no, as ##k## is always positive in this context. The equation represents the relationship between mass, acceleration, force, and displacement, where ##k## represents the spring constant.
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?

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 ##.

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

## 1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and always acts towards the equilibrium position.

## 2. What is the sign of k in SHM?

The sign of k in SHM is determined by the direction of the restoring force. If the restoring force acts towards the equilibrium position, k is positive. If the restoring force acts away from the equilibrium position, k is negative.

## 3. Why is it important to know the sign of k in SHM?

Knowing the sign of k in SHM helps us determine the direction of the motion and the equilibrium position. It also allows us to accurately calculate the period and frequency of the oscillation.

## 4. Can the sign of k change in SHM?

No, the sign of k remains constant in SHM. It is a characteristic of the system and is determined by the physical properties of the oscillating object.

## 5. Do we always need to assume the sign of k in SHM?

Yes, assuming the sign of k is necessary in order to accurately analyze and calculate the properties of SHM. However, in some cases, such as when using a mathematical model, we may be able to choose the sign of k that is most convenient for our calculations.

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