This video uses forces and simple harmonic motion to derive the period of a pendulum (for small angles). It also shows why the formula only works for small angles.
Great video but I think gsin(theta) should be negative since it acts in opposite direction to displacement. That way, when you rearrange for T, you don't just magically lose a negative but it cancels out instead
Thanks for watching but I’m a little annoyed this video is doing well because with hindsight the method is technically a little wrong (see other comments for clarification)…if it helps understanding though I’m glad.
Lol I like where your head’s at pi^2/g is pretty close to one…but in defence of physics the g represents the gravitational field anywhere not just near the surface of the earth
This is the best derivation I've seen so far, but I'm a bit confused at 1:38. What happened to the negative sign on the right in -ω²? Could we have defined our mgsinθ to be positive in our diagram to fix this?
Yes exactly…I kind of rolled the negative sign into the value of g but that makes things more difficult to see. Thanks for clarifying that, Honestly, with the benefit of hindsight, I have a few problems with this derivation but it should give you the main idea. One thing I’ll mention is that I just assumed that it was simple harmonic and then worked from there but had I used the sin theta = theta approximation earlier and then substituted theta for X/L it would have been clear as day that the pendulum follows simple harmonic motion. Then I could have set the acceleration equal to the defining equation and moved from there. I recommend you try doing it that way to get the concepts in.
Oh wow…thank you so much for sharing! It makes me really happy to know you guys are interested in learning where these things come from rather than just memorising them. Physics should make sense and I’m glad you guys put the effort in.
@@TheBrainFiller we do this for every proof we see and we've been having lots of fun! Usually Sal from Khan Academy covers these but sometimes there are gaps and we get confused. Thanks again ^^ Uh oh.. what happened to our first comment?
from my prespective... it goes positive because it's squred. so when it's swicth into root form it goes positive. even if its negative after squared, it will go postive if its divided by same value.... BTW.. if there's mistake please comment..
Um so the point of the formula is that it’s actually independent of the starting angle. So, if you were given the length of the pendulum and the constant g, that’s all you need.
Yeah I’m not really gonna disagree on that…I’ve added some comments to other peoples questions where I talk about how it could have been better presented (I’d have a look at those comments if you want some clarification). Feel free to ask if you have any additional questions (I’m a much better physicist now than I was then)
