Difference Between Harmonic & Nonharmonic Motion: Explained

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In summary, harmonic motion can be reduced to a sine or cosine function and is characterized by a restoring force that is proportional to displacement. Simple harmonic oscillations, or SHM, are a type of harmonic motion that can be described by the equation F = -kx or a = -(k/m)x. This motion can be derived from the equation x = Acos(ωt), v = -ωASin(ωt), and a = -ω^2(Cosωt). All types of oscillations, including SHM, need to be analyzed and are considered the 'simplest' in mathematical terms.
  • #1
deadlytrogdor
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I feel like I should know this but I'm not sure that I do...

What is the difference between harmonic and nonharmonic motion? I did a quick google of this, but I didn't find it helpful...

The most helpful thing I read was that harmonic motion can be reduced to a sine or cosine function. Is that correct?
 
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  • #2
Use the word 'oscillations'.
All types of oscillations need to be analysed... agreed?
The 'simplest' ,in mathematical terms, are Simple Harmonic oscillations or SHM
What makes them 'simple' is the condition that restoring force is proportional to displacement.
ie F =-kx, or acceleration a = -(k/m)x
You know that a = dv/dt and v = dx/dt so this motion can be derived from motion where x=Acos(ωt), so v = -ωASin(ωt) and a = -ω^2(Cosωt)
 

FAQ: Difference Between Harmonic & Nonharmonic Motion: Explained

What is the difference between harmonic and nonharmonic motion?

Harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. This results in a sinusoidal or wave-like motion. Nonharmonic motion, on the other hand, does not have a restoring force that is directly proportional to the displacement and therefore does not result in a sinusoidal motion.

How can harmonic and nonharmonic motion be distinguished?

One way to distinguish between the two types of motion is by looking at the shape of the displacement-time graph. Harmonic motion will have a sinusoidal shape, while nonharmonic motion will have a non-sinusoidal shape. Additionally, harmonic motion will have a constant period and frequency, while nonharmonic motion will have a variable period and frequency.

What are some real-life examples of harmonic and nonharmonic motion?

Harmonic motion can be seen in simple pendulum motion, mass-spring systems, and the vibration of a guitar string. Nonharmonic motion can be seen in the motion of a rollercoaster, the swinging motion of a child on a playground swing, and the motion of a bouncing ball.

How do the equations for harmonic and nonharmonic motion differ?

The equations for harmonic motion involve trigonometric functions, such as sine and cosine, to describe the motion. The equations for nonharmonic motion can vary depending on the type of motion, but they often involve more complex functions such as polynomial functions.

Can a system exhibit both harmonic and nonharmonic motion?

Yes, a system can exhibit both types of motion. For example, a mass-spring system can exhibit harmonic motion when the spring is stretched or compressed, but it can also exhibit nonharmonic motion when the mass is released and experiences friction or air resistance.

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