Simple Harmonic Motion(SHM) - Position Equation Derivation
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- Опубликовано: 21 июл 2024
- Deriving the position equation for an object in simple harmonic motion. Want Lecture Notes? www.flippingphysics.com/shm-p... This is an AP Physics 1/JEE/NEET topic.
0:00 Reviewing circular motion vs. simple harmonic motion
0:24 Defining x position
1:13 Using angular velocity
3:18 The position equation
3:31 Visualizing the position equation
5:16 The phase constant
6:49 Angular frequency
Next Video: Simple Harmonic Motion - Velocity and Acceleration Equation Derivations
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- I sottotitoli di questo video didattico di fisica sono stati tradotti in italiano. Grazie alla classe della Prof.ssa Garagnani!
Previous Video: Comparing Simple Harmonic Motion to Circular Motion - Demonstration
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Thank you to Christian Politis for transcribing the English subtitles of this video.
#SimpleHarmonicMotion #Position #Derivation
Why is this channel so underrated?
I wish I knew the answer to that one.
Beacuse of way of teachings
@@FlippingPhysics really brother you saved me many times... Your way of teaching is really awsome
Calculator in Radian mode when using simple harmonic motion equations.
Calculator in Radian mode when using simple harmonic motion equations.
Calculator in Radian mode when using simple harmonic motion equations.
I will never forget !
What a incredible video! Everything makes sense now. Thanks for the brilliant explanation
You're very welcome!
thank a lot man!! , I have been stuck at this part for the past 2 weeks watching video after video to understand the concept, but you just explain it within 8 min in the most crystal clear way . I cant thank enough man ♥♥
the physics GOAT. i know you will reach 1 million+ subscribers one day. I can feel it!!!
This is so amazing. I thank you a lot. I understood this intuitively!
Really this helps me a lot .... Visualising everything clear my doubts...thanks alot
hello, i have a physics quiz tomorrow and your videos really help me a lot in understanding the concepts. I love the visuals too! It makes the concepts so much clearer. Thank you to your channel 💗
You are very welcome. Glad to help you learn!
Super amazing video sir. Today i saw and got it really interesting. Love from INDIA 🇮🇳❤️
Great visualized explanation ... It helped a lot thankss ❤️
Simple explain method, Thanks for your effort ❤️❤️❤️
Thank you! You made it easy to understand! I was stuck on how to write the position equations from the graphs given and you helped me!
You're very welcome!
Thank you for creating these videos You help me a lot throughout this quarter.
You are welcome.
The visual illustration is awesome !
Thanks!
dont stop sir
What a great explanation man!! Thank you🙏🙏
You are very welcome. Glad to have helped you learn!
thanks, this really helped with a lab problem!
Thank you so much for your help!
Your videos are the best!
Glad you like them!
Your videos are so helpful, I wish I had access to these types of videos when i was in high school and university. I have a BSc. in Physics but honestly i never understood a lot of things in Physics at university and high school. I got through university mostly by cramming and memorizing what to do when questions are structured a certain way. Started private tutoring just to make some extra money but when students asked me certain questions there were times where I was not able to explain to them because i never understood it myself. Your content helps me to understand all the things i never understood in Physics and when you truly understand something you tend to remember it for a longer time. So thank you for sharing and big up from Trinidad!
I am humbled by your wonderful comment. Thank you for your kind words.
Hats off to you. Really incredible videos and awesome and effective way of study. Thankyou Sir😍
Thanks for the compliment!
Very nice job - super super video.
Thank you very much!
we have this in my syllabus and its a fraction of our chapter . but presentation is top notch
This is one of my most favorite physics channels!!contents are just amazing!Really appreciated your hard work sir!!May Allah bless you.
Thank you for this lovely comment.
Wow this helped me finally understand the concept of that equation and how it all relates back to the circle stuff thx
Glad to help!
Amazing and very interesting way of teaching . its really very helpfull
Glad you think so!
Your teaching is awesome.
Thank you! 😃
Soo good!
greatrly understood than one hour lecture
U are saving me from the wrath of killer JEE & NEET physics ... just a suggestion,would u mind solving the physics section of one of those papers here ? with animation and stuff ......will make my life easier
You are very smart i wish if i were like you and please any suggestion of physics book
very informative...
Awesome explanation
Thanks!
imagine if every student in class answered the teachers question accurately and respectively like this
Well I will still fail my final, but at least I know to use radians now since that was never mentioned to us in class :D Thank you!!
Great, sir.
Glad you enjoyed.
Thanks
Thanku sir 🙏🙏❤️❤️🥰🥰
How come r*Cos.theta(degrees) = r*Cos.theta (radians) ??? Can we shift from degree to radians just like that?
By definition, the same angle in both units should have the same sine and the same cosine, when you configure your calculator for a mode that is consistent with the angle unit. 60 degrees and pi/3 radians are both the same angle. So sin(60 deg) must equal sin(pi/3 radians), due to the fact that 60 deg = pi/3 radians. The conversion factor is 180 degrees = pi radians. To convert 60 degrees to radians, multiply by 1 in a fancy way. 1 = (pi radians)/(180 degrees). 60 deg*(pi rad)/(180 deg), degrees cancel, and we are left with pi/3 radians.
thanks sir
wow tnk you 🇸🇴🇸🇴🇸🇴🇸🇴
LOVE FROM INDIA
it was interesting
Before watching this clip I thought I understood something. Now I'm totally confused.
Hey Why is x(t)=Acos(ωt+ϕ).
And Why isn't this part described
It takes the background of differential equations to derive this from first principles. However, knowing the solution in advance, we can show why this is the case, and only need the background of Calculus and Trigonometry.
We desire to satisfy the equation x"(t) + K*x(t) = 0, which is the form that our equation of motion takes, when deriving it from Newton's laws. Note that K is not necessarily the spring constant, but rather the constant of proportionality between acceleration and position. In the mass/spring example, K=k/m.
Solution known in advance:
x(t)=A*cos(ω*t+ϕ)
Use angle sum identities to convert this into sine and cosine:
cos(ω*t+ϕ) = cos(ω*t) * cos(ϕ) - sin(ω*t)*sin(ϕ)
Define constants B and C, such that B = A*cos(ϕ), and C = -A*sin(ϕ). Since ϕ is a constant, it can be embedded in as part of the leading constants of each trig term. We now can write our formula for x(t) as:
x(t)=B*cos(ω*t) + C*sin(ω*t)
Take the first derivative of x(t):
x'(t) = -B*ω*sin(ω*t) + C*ω*cos(ω*t)
Now take the derivative again:
x"(t) = -B*ω^2*cos(ω*t) - C*ω^2*sin(ω*t)
Factor out -ω^2:
x"(t) = -ω^2* (B*cos(ω*t) + C*sin(ω*t))
Recognize the factor on the right side is equal to our original function for x(t), therefore:
x"(t) = -ω^2 * x(t)
Plug this in to the differential equation we are trying to solve:
x"(t) + K*x(t) = 0
-ω^2 * x(t) + K*x(t) = 0
And you can see that when ω^2=K, our differential equation is satisfied by any linear combination of sin(ω*t) and cos(ω*t). All linear combinations of sine and cosine of the same input, can be re-written as A*cos(ω*t+ϕ). The essential difference between sine and cosine is a phase shift, as is the difference between cosine and any linear combination of sine and cosine.
@@carultch how old are you bud?
@@lawliet2263 34. Any particular reason you are asking?
@@carultch i read your other comments and could tell you're either a professor in physics or just who knows physics at a completely different level than an average joe
best
I think I'm the dude in the middle, ...but I would've gotten the answer wrong... :( Thanks for the lesson.
thank you so much! i have an test tmr and this helps a lot!
ᶦ ʷᵒᵘˡᵈ ˡᵒᵛᵉ ᵗᵒ ˢᵉᵉ ᵐᵒʳᵉ ᴵᴮ ᵖʰʸˢᶦᶜˢ ᶜᵒⁿᵗᵉⁿᵗ :⁾
Best of luck on your test tomorrow!
(lots of my videos are on IB topics)