What assumptions do I need for a simple gravity pendulum?

What assumptions do I need for a simple gravity pendulum?

I know the bob needs to be regarded as a particle. The rod needs to be massless and of constant length. And we ignore air resistance and friction.

But what other assumptions do I need in order to allow the derivation of an equation of motion from, say, Newtonian mechanics?

EDIT

After searching some more online, the only seemingly useful information I could find is this https://en.wikipedia.org/wiki/Pendulum_(mathematics)#Simple_gravity_pendulum

Is it accurate?

• The rod must not bend... You want no forces other than gravity, but I think you've covered that. Commented Apr 24, 2018 at 22:53
• Rigid systems with non-trivial mass distribution are just as easy as a simple pendulum if treated in terms of moment of inertia and torque, so you don't even need a point-like bob or a massless support. Commented Apr 24, 2018 at 23:43
• @dmckee I see, yes. But the energy conservation properties of a simple pendulum, when those two assumptions are made, is much simpler to apply. And results obtained with them don't deviate too much from experimental data. Commented Apr 24, 2018 at 23:58
• Steven I can formulate the so-called "physical pendulum" in exactly the same way. Not that it's obviously better, but it is more general, and you seemed to be interested in the minimal assumptions. Commented Apr 25, 2018 at 1:20

You need to assume small swing amplitude or face nonlinear behaviour :-) .

• Really? Even without friction or air resistance? Why? Commented Apr 24, 2018 at 22:41
• The equation of motion is $ml\ddot{\theta}=mg \sin \theta$. This reduces to a harmonic oscillator only for small $\theta$. Commented Apr 24, 2018 at 23:01
• I see. I can't use small angles, so I'll face the non-linear behaviour. What are the assumptions of that? Commented Apr 24, 2018 at 23:49
• After searching some more online, the only seemingly useful information I could find is this en.wikipedia.org/wiki/… Is it accurate? Commented Apr 25, 2018 at 0:30
• I think you can safely rely on it. Commented Apr 25, 2018 at 17:07

Well, most of the times we assume that gravity is purely acting downwards, while due to the earth not being flat it will vary a bit if the pendulum moves. It goes without saying that this effect is negligible and seldom considered.
For a perfect pendulum you also demand that the rod does not stretch during the oscillations.