Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

Content Times:
0:00 Simple Harmonic Motion Review
1:57 Simple Pendulum Definition
3:28 Pendulum Restoring Force
4:45 Net Tangential Force
5:47 Bringing in Arc Length
7:20 Small Angle Approximation
9:10 Solving for Angular Frequency
10:03 Solving for Period
10:32 Position, Velocity, and Acceleration
12:03 Angular Velocity and Angular Frequency in the same equation?

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#Derivation #SimpleHarmonicMotion #SimplePendulum

[oliviabranson]

Your videos constantly make me have "aha" moments. You explain things super well. Thank you!

[Kenzo_]

You're the best teacher. Thanks a million 👍

[sammundays]

small angle approximation part helped me out so much thank you

[hagoraashraf]

This is just the week before my final exams in my first year at STEM high schools and this video explains the last L.O and it's just on time.
Edit: Thanks a lot for the video and the like ❤❤

[ammarm]

I like your videos. Very much better and interesting.

[zabuza]

Thanks for sharing. Not sure if you take requests from your subscribers but if you do, I would love to see some videos on operational amplifiers

[khanhhuyen]

7:03 L = ds/dθ => L ^2 = (ds/dθ)^2
why u write L?

[SamkeloSam-vvii]

What does " del T" mean while completing a table in simple harmonic motion .i know T is a period but that del confuse me

[petromyzontida.]

please try to keep the simple, creative neumericals for nerds.

[NefariousPear]

Can someone please help me! My brain has died a thousand deaths trying to figure this one out.
Assume 1.6m cable length and .087rad amplitude (140mm). The angular frequency and period I get using the small angle approximation is 2.47rad/s and 2.5s respectively. Would that not equate to an arc length per second of 3.952m/s?
If I work out arc length per second from period and amplification (T/(A*4)), I get .1344m/s which seems more reasonable. How have I screwed this whole thing up?

Are radians in angular frequency for simple harmonic motion referring to a different angular displacement than the radians for everything else? It consistently results in about 2pi radians per period no matter what i do with the numbers, which makes me think it is referring to the arc length of a period divided into 2pi segments... How did I get so far away from such a simple assumption?!