The name simple harmonic motion suggests that its the simple version of "harmonic motion".
Does harmonic motion exist and if so is there a difference between these 2 terms?
[Physics] Difference between harmonic motion and simple harmonic motion
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In the case of a simple pendulum (also called a mathematical pendulum of simple gravity pendulum), one assumes that all of the mass is the bob and the rest of the pendulum is massless. An example of the simple pendulum is given in the image below.
The simple pendulum (see wikipedia or hyperphysics) leads to a simple differential equation by using Newton's second law: $$\ddot{\theta}+\frac{g}{l}\sin(\theta)=0.$$
This pendulum gives the easiest way te look at harmonic motion. The above case is what they call the simple pendulum.
You could add an extrernal source so it would be a driven simple pendulum, of friction so that it becomes a simple pendulum with friction.
If you want to further complexify it, you could drop the assumption that all of the mass is in the bob and add inertia to the picture (so a real-life pendulum). This kind of pendulum is called the physical pendulum (or compound pendulum), the swinging body is no longer considered a point mass, but a mass with finite measurements. An example (compared to the simple pendulum) is given on the figure below.
This also leads to equations using Newton's second law applied on angular momentum (just as the ones which were used to derive the equation for the simple pendulum).
Consider the case that you have two oscillators (harmonic or otherwise). It is the case that either
- The oscillators are independent, i.e., non-interacting
- The oscillators are coupled, i.e., interacting
If (1), the differential equations for the system are just two single oscillator equations, e.g., the acceleration of one mass does not depend on the position of the other mass.
If (2), the differential equations are 'mixed', e.g., the acceleration of either mass depends on the difference in the position of the masses.
The term harmonic oscillator is opposed to anharmonic oscillator.
The natural (unforced) oscillation of a harmonic oscillator is a sinusoid, i.e., has a single frequency.
Best Answer
The OP should perhaps have asked "Does simple harmonic motion exist?" given that it is harder to find examples of simple harmonic motion than harmonic motion.
Any motion which repeats itself can be called harmonic motion and so simple harmonic motion is in the set of harmonic motions.
One way of defining simple harmonic motion is via the differential equation
$\dfrac{d^2X}{dt^2} = - \omega^2\,X$ where $X$ is some parameter which could be a displacement, an angle etc.
In mechanics it can be interpreted as the motion of a mass acted on by a restoring force which is proportional to the displacement of the mass from a fixed point.
Simple harmonic motion has important properties, for example, the period of oscillation does not depend on the amplitude of the motion and lots of systems do undergo simple harmonic motion even if sometimes it is an approximation.
A good example of the difference between harmonic motion and simple harmonic motion is the simple pendulum.
The simple pendulum undergoes harmonic motion, however for small angles of oscillation it does approximately undergo simple harmonic motion.