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I have gone through the Phys.SE question Can a simple pendulum be considered a simple harmonic oscillator?. From the 1st answer of this Question it seems to me that another type of "Harmonic motion" is "Damped Harmonic Motion".

But can you please explain what the other type of Pendulum is? Is this Compound pendulum or Damped Pendulum or Something else?

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  • $\begingroup$ For a damped pendulum, you just introduce a term $\gamma \dot{\theta}$ into the equations of motion. $\endgroup$ – JamalS May 22 '14 at 5:41
  • $\begingroup$ Simple pendulum can mean simple compared to compound, or simple compared to one that behaves like a simple pendulum despite large amplitude. Recall the simple pendulum analysis makes assumptions about small motions and very small angle. Check on "isochronous pendulum". $\endgroup$ – C. Towne Springer May 22 '14 at 5:43
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    $\begingroup$ @ C. Towne Springer , see this wikipedia article, here there is no assumption of small swing , but they still write simple pendulum:en.wikipedia.org/wiki/… $\endgroup$ – user22180 May 22 '14 at 5:53
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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

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.

enter image description here

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).

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