Simple Harmonic Motion - IB Physics

I go over the characteristics of simple harmonic motion, using examples of a spring and pendulum. Simple harmonic motion is periodic motion around a central point of equilibrium where there is no net force. There is a restoring force that acts on the object that is directly proportional to the displacement from the equilibrium position and acts in a direction opposite to that displacement.
In physics, we can describe the period and frequency of objects in simple harmonic motion, as well as their position, velocity, acceleration, force, kinetic energy, and potential energy at different points along their path.
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[@andrewtran979]

Top ten physics lectures of all time

[@MathGPT]

You sir are a lifesaver, these are the most aesthetic lectures ive ever seen

[@guneygurbuz8565]

Thanks a lot for the lecture, it really helped me to cover all the lacking parts in SHM!

[@orangecaprinun]

SUBBED! Why did i just find u dude! Whereve u been

[@dominicestebanrice7460]

Sir, after watching hours of content on SHM, this is the best and most useful treatment I've found. Thank you! Q: Is it incorrect to use the vocabulary of INERTIA to explain why the mass swings through the equilibrium point when the restoring force on it is zero.......I am trying to form the proper physics sentences(s) to explain why the mass just doesn't stop when there is no more restoring force on it? It's because of Galilean inertia/N1, right?

[@AndyMasley]

Yes that's correct! It's important to remember that when an object has no net force acting on it, it will continue with whatever velocity it has and not just come to a stop. That's the idea of inertia: it requires force to change an object's velocity. No net force, no change.

[@samerdan6654]

Thanks, needed this!

[@SmellyFish78]

great explanation well done

[@Life-ze1no]

thank you. well done

[@sumeetrathore7946]

Appreciated sir 👍

[@osamaqudah9241]

🐐🐐🐐🐐🐐🐐🐐 may allah bless you brother

[@danielm9463]

At the bottom of the swing, the tension force is larger than the gravitational force by an amount mv^2/r. I know you're presenting a simplified scenario here, but in Topic 6 students learn that moving around a circle requires a centripetal net force. Do your students ever ask how the center position can be 'equilibrium' when there clearly must be a nonzero net force directed toward the center? How do you approach this with your students? I try to get them to the point where they can explain that the tangential component of motion executes SHM (Fnet = -kx) but the centripetal/radial component executes circular motion (Fnet = mv^2/r). I've always wondered what other teachers do, and you've clearly got good content here!

[@danielm9463]

​@@AndyMasley So, the formal resolution is to consider the polar coordinates. In the r-hat direction, the net force everywhere is equal to mv^2/r. In the θ-hat direction, the net force everywhere is equal to -mgsinθ, which approximately equals -mgθ for small angles (where θ is the angular displacement). Simple harmonic motion occurs when the net force has the form -(constant)(displacement), and thus the θ-hat component of motion will display the attributes of SHM.
Since our IB students don't know polar coordinates, I phrase this in terms of the "centripetal component" (or "radial component") and "tangential component." I show the forces on the pendulum when at the edge and ask if it looks like SHM. To answer the question, we break mg into components mgcosθ and mgsinθ, cancel out mgcosθ with tension (because if v = 0 at the edge then the net centripetal force must be 0 at the edge), and realize that F_net = mgsinθ ≈ -mgθ at the edge. So far, the pendulum's net force looks a lot like SHM (where F_net = - [constant][displacement]). Then, we analyze the forces at the center and realize that F_net = tension - mg = mv^2/r ≠ 0. But even though this violates SHM, we can restore the idea that F_net = -(constant)(displacement) by restricting our analysis to the net *tangential* force, because at the bottom of the pendulum's path, the net tangential force is 0.
The conclusion, then, is that a pendulum's centripetal motion is governed by circular motion F_net = mv^2/r, and the tangential motion is governed by SHM F_net = -(constant)(displacement). I think many follow the discussion, but we don't spend enough time on it for everyone to really solidify those subtleties in their minds.

[@danielm9463]

@@AndyMasley No problem! If you try this out or put it into a video, I'd love to hear how it goes with your students. I've got a video that kind of shows a little of this, but I've been wanting to re-do one that distinguishes the ideas more clearly. Would be interested in your experiences with students on these ideas!