What is the connection between simple harmonic motion and pendulum motion?

AnthroMecha

1. The problem statement, all variables and given/known data

What is the connection between simple harmonic motion and pendulum motion?


2. Relevant equations

Harmonic motion period=T=2piroot(m/k)
Pendulum motion period=T=2piroot(L/g)

3. The attempt at a solution

Conservation of momentum??

Thanks for any help!!

Delphi51

I strongly suggest reading the Wikipedia article on simple harmonic motion.
Consider comparing the equation of motion for the general SHM and the pendulum, that is the formula relating angle or displacement to time.

AnthroMecha

Thanks for pointing me in the right direction. This is what I came up with:

A pendulum oscillates in a simple harmonic motion like that of an oscillating spring. The angle θ in pendulum motion is relative to the distance x that a spring is stretched by a mass (m) and a gravity (g).

Delphi51

Pretty good. But isn't SHM a general concept of which the pendulum, spring, water waves, radio waves, etc. are all specific examples? For the word "connection" in the question, I would look for what makes the pendulum simple harmonic, both from the motion characteristics and the nature of the force that causes the motion.

AnthroMecha

Hmmm...a restoring force in the opposite direction of displacement is what makes it a SHM, right? and in the case of the pendulum mg is the restoring force?

Delphi51

The restoring force has to have a specific formula. . .
Yes, mg is the driving force, but it isn't in the right direction, is it? The pendulum restoring force is a little bit complex, and when you get into the details it is only approximately the right formula, so the pendulum only has nearly SHM when a particular condition is met. No doubt you can look up all that if you want to give a great answer.

AnthroMecha

Thanks for the help Delphi!!

Delphi51

Most welcome!