Simple Pendulum: Understand the Relationship Between Theta & L

[SebastianRM]

1. Homework Statement
Hey guys, I am reading my Physics book, in that specific section it says "the restoring force must be directly proportional to x or (because x=(theta)*L) to theta"

Homework Equations

The Attempt at a Solution

I have tried to look for that x=(theta)*L relationship online; however, I was not able to find it. I was hoping someone here could explain that relationship to me.
Thank you.

 

[mfb]

Did you draw a force diagram? It should become clear from that.

 

[SebastianRM]

Yeah it comes with a diagram, but i do not see how multiplying L by the displaced angle, I can end up with the length of the arc. Like, how the unit conversion works. for that? With the diagram I can see where the the restoring force in the pendulum comes from though.

 

[mfb]

The arc length is L*theta by definition of the arc length or the angle.
For small angles, this is approximately equal to the horizontal displacement as well.

 

[SebastianRM]

And how would the unit conversion work that by doing the equation, it provides the arc length?

 

[haruspex]

And how would the unit conversion work that by doing the equation, it provides the arc length?

I'm not able to parse that question, so I'm not sure what you are asking. The angle must be provided in radians. The definition of the radian is that if the angle is measured in radians then multiplying it by the radius gives the arc length.
Of course, if x is the horizontal displacement then that is not the same as the arc length, but as mfb posted they are approximately the same for small angles.