Simple Harmonic Motion, Mass Spring System - Amplitude, Frequency, Velocity - Physics Problems
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- čas přidán 8. 09. 2024
- This physics video tutorial explains the concept of simple harmonic motion. It focuses on the mass spring system and shows you how to calculate variables such as amplitude, frequency, period, maximum velocity, maximum acceleration, restoring force, spring constant k, elastic potential energy, kinetic energy, and mechanical energy in addition to describing the motion of the mass spring system using a sinusoidal function such as sine or cosine. This video contains plenty of examples and practice problems.
Intro to Pressure:
• Introduction to Pressu...
Fluid Pressure Review:
• Fluid Pressure, Densit...
Simple Harmonic Motion:
• How To Solve Simple Ha...
Energy In a Simple Harmonic Oscillator:
• Energy In a Simple Har...
The Simple Pendulum:
• The Simple Pendulum
_______________________________
The Physical Pendulum:
• Physical Pendulum Prob...
Mechanical Waves Problems:
• Mechanical Waves Physi...
Wave Speed on a String:
• Wave Speed on a String...
Standing Waves on a String:
• Standing Waves on a St...
Speed of Sound In Matter:
• Speed of Sound in Soli...
Sound Intensity Physics Problems:
• Sound Intensity Physic...
_______________________________
Sound Intensity Level:
• Sound Intensity Level ...
Beat Frequency:
• Beat Frequency Physics...
Standing Waves In Organ Pipes:
• Standing Waves In Orga...
Doppler Effect Physics Problems:
• How To Solve Doppler E...
Sound Waves Review:
• Sound Waves, Intensity...
Physics PDF Worksheets:
www.video-tuto...
Here is a list of topics:
1. Simple Harmonic Motion - SHM Horizontal & Vertical
2. Vibrations, Oscillations, and Periodic Motion
3. Simple Harmonic Oscillator - SHO
4. Restoring Force and Equilibrium Position
5. Hooke's Law of Springs - Force vs Displacement
6. Work Required to stretch or compress a spring
7. Stiff vs Loose Springs - Spring Constant K - Proportionality Constant
8. Maximum Displacement and Amplitude
9. Cycles and Vibrations - Period and Frequency Calculations
10. Work Force Displacement Graphs - Area Under Curve - Calculus & Integration
11. Elastic Potential Energy of Springs
12. Maximum Kinetic Energy vs Minimum Velocity
13. Mechanical Energy - Total Energy of the Spring-Mass System
14. Maximum Velocity Formula
15. Maximum Acceleration Equation
16. Velocity Function of X - Displacement Equation
17. Sinusoidal Functions - Describing the Motion of a Oscillator Mathematically Using Sine and Cosine Functions
18. Finding Amplitude, Period, and Frequency From Sine and Cosine Functions
19. Writing Sine and Cosine Functions For Position, Displacement, Velocity and Acceleration
20. Simple Harmonic Motion and Circular Motion
21. Period, Frequency, Mass, and Spring Constant K Formulas
22. Car Spring Problem
23. Spider Web Spring Problem
24. SHM - Position Function of Time
25. Omega - Angular Velocity and Frequency
26. Position, Velocity and Acceleration Sinusoidal Functions - Derivatives and Calculus
27. Damped Harmonic Motion - Overdamped, Underdamped, Critical Damping
28. Forced Vibrations and Resonance
29. Natural Frequency vs Resonant Frequency
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![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
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0:20 Mass spring system
1:50 Hooke's Law
2:29 Spring constant
5:07 p1
8:35 p2
13:45 Oscillator
20:09 Energy
22:01 Mechanical energy
24:29 Maximum velocity
25:37 Maximum acceleration
26:20 velocity as a function of x
29:17 frequency and period
32:29 p1
35:04 p2
42:26 p3
51:15 p4
58:20 equation for period and frequency
1:09:10 p1
1:12:20 p2
1:14:51 p3
1:20:54 p4
1:22:55 p5
1:24:30 Equations describing motion (x,v,a)
1:33:53 p1
1:43:42 p2
1:51:22 p3
1:57:13 Review
1:58:05 Damped harmonic motion
2:01:31 Resonant Frequenc.
thank you soo much
you legend, thank you.
Thank you.
respect
You are an absolute legend. Thank you.
Bro,I just wanna have a moment to say thanks, without you my life was very hard, the moment I came across your channel,I was changed forever and I was one of the best student at my school, I got "A"s in Mathematics, Chemistry and Physics and "B+" in Biology. Continue doing the good work, May God bless you man 🙏
my physics teacher is awful, he just gives us worksheets and doesnt teach, thank you for being my savior
I wanted to share my working just incase if someone confused at 1:50:05
@1:50:05 The question is asking for velocity, acceleration, and restoring force at x = 0.5m
We know Vmax = 18.6 m/s and A = 1.5m and set the calculator in radiant mode
Method 1 -- By subs x = 0.5m into the formula v(specific time) = Vmax * sqrt(1 - x^2/A^2) This gives V(at x=0.5) = 17.536 m/s
Methods 2 -- If we want to use the V(t) equation we have to find the 'time' when the block at x=0.5
Using x(t) = 1.5 * Cos (12.4t), we subs the value 0.5 = 1.5 * Cos (12.4t), this gives t = 0.099271s
Thus, subs t = 0.099271s into V(t) gives v(0.099271) = 18.6 Sin (12.4 * 0.099271) = 17.536 m/s (Same answer as Method 1)
This has been discussed before in the comment section but I hope I could clarify this again.
I also wish someone could correct my working if I made any mistake.
Thanks a lot
you are excellent and it's difficult for me to say you made a mistake but you made a bit mistake when you find time t at x=0.5 and t at that position becomes t=5.6878s and as you do by substituting t=5.6878s into V(t)=-18.6Sin(12.4t) it gives V(5.6878s)=-18.6Sin(12.4*5.6878)=-18.6Sin(70.52)=-18.6*0.942=-17.53 m/s
If I made any mistake ,anybody could correct my working.
Thx man I also got very confused but this clarified it
Thanks I was really confused there before
Then a=76,879999874~=76.88m/s^2?
*I get i'm 4 years late on this, but each individual category having a timestamp would be very helpful.*
I'm one year late but it's okey
The top comments already helped with that
Look at 2nd top comment
Yes, yes its the topic comment jsut look when he posted this question it says a year ago and the time stamp was 11 months ago so it was relevant then
This was a really intimidating topic for me, and the way you taught it made me finally feel like I understand it. Specifically, the way you gradually introduced new stuff. By the time you introduced period and frequency I was confident I could use the energy equation. And by the time you start graphing sines and cosines I'm already blasting trough the frequency problems. Thank you for the time you put into the lesson!
You are one of the best CZcams teachers for math, physics and chemistry. I really appreciate your dedication to teaching. Thank you very much.
Whether you see this or not, i owe my Marks to you.
You've been making me pass my academics from the beginning of varsity and i thank you hey. Your help is much appreciated ✨ 🔥
Thank you
This is a life saver. I have HSC in about 45 days and have always had trouble with SHM and springs. But after this lesson, I am very confident about it and will boldly attempt any problem that comes my way . Thanks man !
do you know everything, physics, maths, how do you do? you are the best!
Respect🎩
Also chemistry and biology
This guy should ask for a wage from UNESCO for teaching students all over the world xD
@@hisyamhasbi8257 yeah he's a big GOAT. I attend lecturers just for register then I run to him
Just became a Patron. I encourage others to do the same. These are some of the best tutorials on CZcams. Sal Khan could learn a thing or two from your teaching method.
honestly man your videos have always been a blessing to me and many young people out there struggling to keep pace in a crowded system where students who dont get what is being taught at the instant are called dumb
sure, this also makes me say teachers who cant get students to understand on the first attempt too are dumb
your videos are just transformational and they should be used in classes and schools to aid understanding
Keep up with the good job. Love you guys soooo much
That is so true..he makes me feel like I've learned the topic detail by detail, perfectly. And it's so real..every second. My friends sometimes sarcastically say things related to me being a duller and also lazy because I don't practice because of online friends . It's 10:21 pm, I haven't started studying yet, since 6:30pm. It's very heartbreaking. I can't understand and focus well physically, where there are noisy brats, slow explanation, just all that tension I can't bear and could start to cry anytime soon. The Organic Chemistry Tutor is one of the channels who helps me a lot and provides more interesting information. Very glad!! Hope I'll really become a smart student...I feel devastated, all my school mates called me as topper topper, because I wasn't lazy, wasn't overthinking, was studying consistently. It's the opposite now, and college mates think I'm the worst. I always get the last rank even i can't believe it. Straight A to negative marks student. Very.. devastating.
I can do it though. Although it feels like a stab through my heart. I love learning.
Sorry for the emotional rant.
I have a test in about 4 hours lol. I really needed a good review of periodic motion and oscillation. Thank you so much! And for always saving the day 🎉
How was your exam
@@user-fh2rw9zh8g I did well on it!
This channel is the best channel for all engineering students. Sir, I don't know your name or country, but I learned most of my engineering topics from this channel. Thank you so much for your videos.
Julio Gonzalez
USA
your videos are the best! I like how you derive all the formulas very thoroughly so that we can understand where they came from. My textbook is very brief on derivations so this is great. Thanks so much!
In the 56:45 example I Don't understand why the speed of the mass is not zero as soon as we release the spring
BTW I always watch your videos and I like them so much
It should be 0, this seems to be a mistake. Since x=A, the PE=Total Energy, and KE=0.
There is another mistake during the problem at 1:50:00, x=0.5m and he plugs in t=0.5 for the t in the x(t), v(t), and a(t) functions. You need to solve for t, then plug that number in. I think the correct answer is, at x=0.5m, v= -17.54 m/s and restoring Force = -42.28 N.
Thanks man u saved my life my physics final was fair and to everyone with exams good luck
The 2hrs I spent watching this video was worth it.
Thank you very much 🙏🙌
54:16 I might be wrong, but wouldn't ME = KE + PE and KE = 0 because all the energy is in PE? I think what you found was the speed when the block was at the equilibrium point
Same remark
I have to say that your explanations are amazing ... thank you for breaking this topic into several points.. man you covered everything.. thank you.. your job is very appreciated.. keep the good job up.. God bless yo
Explanations are always so clear and helpful. Serious life saver :)
@1:49:50 , you plugged in 0.5 as time to find the velocity and acceleration , whereas 0.5m was the displacement .
Can you please tell me your answer so I can compare it with mine
You should've plugged it into the first one and solved for t and then plug the t value into both equations
yup. 1:50:50 im having trouble computing Fr using -kx as it’s not matching your answer using F=ma
They are
t = 0.099s
v = -17.65m/s
a = -77.61m/s^2
Fr = -42.68N
(I think)
Ohh I was so confusrd for that, i thought I wasn't understanding something. anyways how do you get the t if it is inside of de cos multiplying by something?
whos here because physics makes you want to cry and memorizing equations for entry exams also makes you want to cry?
I’m failing physics but like- yes
I must say this really helped me a lot... I have the confidence now
Have a SHM test for AP phys tomorrow and I slept through the whole unit essentially. Will come back to update on my grade based off these vids teaching me
Good luck dawg
What did you get?
@@soulsn554 79. Not a great grade but for learning the whole unit the night before I'm not gonna complain to much
Anyone here taking Engineering Physics and trying to grasp the basics? lol
Tomorrow is my final for engineering physics.
I'm taking 101
Final tomorrow - this video legit summed up like two months' lectures
@@carmin. you mean in university?
@@josevilleda15 lmao same
When I ask someone how did you study physics so well, I already know the answer: JG is the hero behind the scene.
This video perfectly shows the frustrating part of physics. There is near zero convention for symbols. f can be frequency, unless it's friction. V can be frequency unless you're using f. And if you're not speaking English then presumably a different letter could be friction.
KE can be kenetic energy but k can also be a constant in Hookes formula which can be written with or without the negative sign depending on your mood. w can be work unless it's actually a lower case omega.
And on and on. How have we not called a meeting and set some damn standards? Any idea on how many people could potentially be contributing to physics but aren't because they give up the first quarter?
Absolutely ridiculous.
The fact you wrote this means you don't understand physics at all. f is frequency and not friction because there's no friction at play here since none of his problems have them and if you took this class you wouldn't deal with friction anyway (maybe a few problems bring it up so you don't forget about the real world, but most of these problems test your understanding of the topics and equations and not about friction). Even if there was friction you can literally write: Friction = [Insert variables and relationships here]. "KE can be kenetic energy but k can also be a constant in Hookes formula" what are you even saying here KE and k are different in spelling. And the sign of k does not depend on your mood but how you set up your problem and axes. There's also a clear difference between W and ω... if you can't differentiate between the letters of the Greek and English alphabet then there's no hope.
Hehe pls.... V²/R can be the equation for Power and the equation for centropetal acceleration :). Funny little equation lol
you're the best when its comes to the explanation
omg thank you soooo much for this video!!! This helped me have an A on my test. I only missed 1 question. not on a quiz but a test!! omg omg thank you. you should teach my AP Physic class my teacher isn't good at explaining thing. Anyway thank you!!!!!
This video is genuinely beautiful!!
THANKS KING!! I have a physics exam tomorrow and this is such great review/practice and everything feels so much clearer now!
How did your physics exam go? Also king?! 😳
I have a problem with the problem done at 1:49:51, part b. We are asked for the velocity and acceleration at x=0.5, which from what I understand, is displacement. The equations for x, v, and a, are written as functions of time, yet we substituted the x= 0.5 where we should be substituting t=?(something)... were we not supposed to use the equation of x to solve for t first, then substitute the t that we get onto the other equations to get v and a? This is the only issue I have; may I please get clarity if possible?
i think it's an error in the video. I was thinking the same
I thought the same as well because this equation with respect to time not position
i got velocity being -17.54ms^-1, and the acceleration being -76.88ms^-2 instead (I set 0.5 = to original displacement equation the solved for t, then substituted that into the v and a equations.
I was also thinking the same I think you should find the value of t (I found it 5.687) at x=0.5 by using the displacement equation given by the question then you place that t value on the functions we have derived
So wat is the difference btwn A nd x in a question?
I am currently taking a AP physics 1 corse in high school and these videos are my saving grace. tysm for saving my grade!
STOP READING COMMENTS AND WATCH THE VIDEO.
good lucking out
lol okay you got me there
thank u king
Thank.you 😂
WTF
2:37 the spring constant (k) has also the unit of kg/s^2. It is a measure of the stiffness of a spring, the more k value a spring has, the greater the restoring force it produces is, and the more difficult it is to deform.
1:49:35 why did you insert 0.5 m in t? Can we insert length in time function?
Found this SUPER resourceful, tnx a bunch ....... btw, u sound like Eminem
Seriously man sometimes I imagine if I still go to school or I actually school on Ur channel.
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This video is so perfect. Thank you so much. I could barely understand my physics professor but you made it so much easier for me.
I love you so much man, you're the reason i'm not failing
A student from my class called me over to do a group study on this topic tomorrow...
Am an extreme introvert..What to do...... Now am here trying to get prior knowledge.... I bet this video will come I handy....
At 1:49:50 the problem asks us to solve for velocity, acceleration, and the restoring force when x is 0.5m. The functions the first part of the problem asks for are with respect to t = time. They were solved by substituting .5 for t. Was this a mistake or am I not understanding the approach to solving the second part of the problem?
Same here. I was to confused when he put the value of x which is 0.5 as t.
Shouldnt we use the given equation for x then put x = 0.5 then solve for t and then use that value of t for the veloctity and acceleration?
@@kabirhasan995 That is what I did and got values like -17.5m/s and -76.9m/s^2 and thus the value changes for F which is -42.3N
@@kamvamenziwa2751 its been a while so I did the problem again and yes our answers have matched.
uhh the comment that i was looking for
@@kamvamenziwa2751 I used a different method I just solved it directly and I am getting the same thing as you too....I was wondering too
i have a question if the derived equation at 1:49:37 is a function of acceleration in terms of time, then why did you use X=0.5 in your subtitution? you substituted 0.5 in a(t)= -18.6 cos (12t). 0.5 is not a time right? please help 😢 he did the same thing too in solving for the velocity at 0.5 meters.
edit 1: i think you should've used the formula on velocity as a function of x. V(x) = - Vmax sq.rt (1-(x sq-A sq)).
Yeah I thought the same too. I got 17.5 m/s
Sir...thank You... you've changed the lives of millions of pp😇😇😇😇😇
I really learnt a lot from this.
Thanks for taking your time to gradually break down the formulas and explaining them
I'm so happy as I've learnt a lot already cos it was like a burden on me before this🤗🤗
i cant find any eacher teachs like you in my life tnx so much sir
im a medicine student and have an elective physics course..
i have to do a presentation on this topic and your video saved me cuz i was so scared of the topic
thx
How did your presentation go? 😃
Your explanation is brilliant! I understood more than at the school.
you make watching long videos worthwhile . Thank you
Since the online class started this channel really save me in every critical moments in my life. So yeah thanks...
PRECISELY EXPLAINED
THANK YOU VERY MUCH
@45:23 why don't we take amplitude by adding 0.4 & 0.2 since amplitude is equal to the max displacement
Thanks much... People like you are rare.. May the good lord bless you more.🙏🙏💯
Hes not the hero we deserve, but the hero we need
midnight physics and chill
What we are anticipating for the most in this two hours video Thats it for this video hope you understand Thanks sir for the two hour free lecture on SHM
Why are u our best teacher forever?
You will live a very long and healthy life. God bless you
You are my hero mate. Would be lost without your videos.
once again my life is saved thanks to you
Could you please make a video for simple Harmonic motion using this equation x(t)= Acos(wt+phi), with showing some examples?
Very very very very very very very helpful for me
The world's best teacher thanks sir
Thank you, Sir. this is great..!
I entered ignorant of these topics, i exited with showering knowledge. Tnx! Kudos. ❤️❤️
the question at 51:38, wouldn't the speed be 0 since it was just released, and the Kinetic Energy equal to 0?
But instead you were calculating the speed at equilibrium point, hence, Vmax
Can anyone explain to me
He wasn't calculating speed at equilibrium point.
note that the spring was compressed {to the left}. due to the compression, the spring gains some energy. when the applied force used to compress the spring is then removed, the energy in the spring will be converted to the kinetic energy of the mass
hence, mechanical energy equals kinetic energy
did this help??
I thought it was 0 too because I got 26.5 has the maximum velocity. The mechanical energy equals potential + kinetic, so idk what he's doing because as soon as something on a spring gets released it has 0 kinetic energy but it's acceleration at the highest as well as it's potential energy. Also this information is probably useless to you since ur post was 4 months ago lmao.
Ooh
Thank you so so much...I wish you had a video on single slits and diffraction.Honestly,I understand you best
Your videos are a good supplement to studying on my own. I am familiar with the concepts, but you explain it more which helps. Have you made a video on differentials? I understand derivatives and integrals, but the differentials in all the physics equations are still a mystery. (all the dx dV dm dt stuff)
Same, he's a good supplement to personal revision
I really really appreciate your effort , thank you very much 💙
بالتوفيق
Life and time saving lessons exist here!
Excellent presentation of one of the most fundamental topics in Physics❤❤❤❤
Your teaching skills are fantastic...but there might be a slight mistake @ 1:50:29 where you have put t= 0.5s whereas it should be x=0.5m as mentioned in the question.
If that is a mistake, do you think it would change the answer. Mine don't match his. I used the v(x) and a(x) equations he derived earlier. V(x) = V(max)(1-(x^2/A^2))^1/2 and A(x) = (Kx)/m.
but isn't the equations derived a function of time?? i also have the same problem
x(t)=Acos(2pift)
v(t)=-Vmax.sin(2pif)
a(t)=-amax.cos(2pif)
and we are given x=0.5 so doesn't x mean displacement and we need to use the first equation and solve for t then sub t in the 2nd and 3rd equations?? please help me.
mthokozisi njapha
I have no idea how we would take " 0.5 = 1.5cos(12.4t)" and solve for t. I guess you could just make a ton of guesses. I feel like it was supposed to say "t=0.5s". I wish he would respond.
mthokozisi njapha
I got t = 5.6878048s by graphing 0.5 = 1.5cos(12.4t) and y = 0.5. 5.6878048 is the intersection point.
well 0.5=1.5cos(12.4t)
*divide both sides by 1.5
0.5/1.5=cos(12.4t)
*shift cos
arc cos(or shift cos)(0.5/1.5)=12.4t
*make t the subject of the formula
t=(cos^-1(0.5/1.5)/12.4
t= 5.687804788
therefore we can conclude by saying t is approximately 5.69 seconds
I have a query. In the "Equations describing motion (x,v,a)" P2, you found the velocity and acceleration with respect to the distance/displacement which is the 0.5m. I think you were supposed to solve for time, then use that value to find velocity, acceleration and the restoring force.
Because even if you calculate the restoring force using the formula Fr=-kx(with k=84.568N/m and x=0.5m), the value calculated will not be the same as the one you just calculated.
can u be generous enough to share your ans with me since i want someones answer as reference to that question as i noticed the mistake as well, my answers are v=17.5362 a=-153.7566 Fr=-84.5661
thanks. ur teaching is awesome. I now flow on my physics tutorials
Great video! I just have one question, why did you plug .5 in the equations for one of the last problems if it is distance and not time? Thanks
Sir..Plz make videos on Electronics and electronic devices... TopicsLike logic gates, transistor, amplifier , oscillator,some concept on semiconductor..Etc..And also numericals based on related topics..My medical exam is nearby..
U are the boy u are best for chemistry and physics that the vedio u have seen before i get everywhere and thanks for yr help boy thanks from my deep heart
Thanks sir for all you do, your video has really helped me a lot. Pls sir can you make a video on damped oscillations
Thank you for making such amazing and helpful videos! Do you have any videos on how to find the dampening constant?
man i like your videos i even hear you batter than i hear my lecturer... thanks... and keep the good work
thanks alot this was an exceptional video
If it is possible, next time could you please write the example questions one line lower. The title of the video always obstructs my view of the question when i pause it.
What's VCL
After Pausing The Video, Tap On The Side Of The Video ,It Would Go
Of you tap on the screen it removes overlay, for me anyway. Hope it helps. I watch everything on my phone though.
No
SIR u are an aboslute legend in my book. hats off to u sir. may u live another 100 years educating the masses and may u attain nirwana ( if u believe in those bullshit )
1:49:30 is not t=0.5, but x=0.5
@baris celik u r ✔❗
beauty of explanation is unexplainable
Those explanations at the end😍😍
God bless you, thank you for helping us
8:32 0.5m since x has to be in m
Bless your heart mate
Thank you so much for these videos I would have have a 40 in my physics class and be grounded forever if you didn’t make these
You're the best, and the best is you. Keep it up
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Thanks a lot . It is too beneficial......but I got confused when you subistituded 0.5 which is x(displacement)in time in the question that starts with a 0.55 kg block......
You are amazing bro👏👏👏keep it up
you have really shown light in my education🙏🙏🙏🙏
Your beauty is amazing.