Simple Harmonic Motion

A description of Simple Harmonic Motion, including its definition, and examples of SHM in the form of oscillating springs and pendulums.

[@abdulqadirtirmizey2727]

Sir, By grace of Allah and your helping videos, I have scored B-Grade in my A-level Physics Exam. By the end of January, I was totally zero at Physics and scored lowest in class. And by the start of February, I started watching your A-level revision videos. Since, I didn't scored well in my AS-Level exams, I was giving composite paper, so the burden on me was double. Believe me sir, by the end of March, I covered the whole syllabus of AS-Level, and 80% of A-level. You know, April is the month of tests for A-level student, and since I had covered almost all of my syllabus, I performed really well in those tests. And then, in A-level exams, I performed excellently. Due to which, I scored B-Grade in Physics. This grade is enough to get admission in Architecture (My dream) and excellent for a student like me :D All thanks goes to you sir, these videos are the reason I scored so well. Thank You So Much.. :D Yours Truly, AbdulQadir Tirmizey

[@madboy1105]

congratz man

[@abdulqadirtirmizey2727]

Thanks Bro.. :D I wish sir could also reply to my comment. But still, your concern is pleasing :)

[@PR0Z0MBIE9877]

You do A-Levels at April?

[@abdulqadirtirmizey2727]

Nope bro... By 'tests' I meant model tests which are taken by your school teachers, for beter practice.

[@kalanijayasekara5285]

How many hours a day did you study? and how did you study? any technique? BTW congrats!!!

[@abhishekshrestha6441]

The "hello" in the start of this video.

[@aurelian3268]

he has achieved Nirvana

[@tendayimbudzi5707]

Davy Jones underrated comment😂

[@xubarney1326]

hahahahahahaha

[@microman99]

Low resolution video, high resolution output concept You save my physics!!!!

[@harolddiaz7046]

You're going to be the reason why I pass my physics classes. You give such good clarity while also being very descriptive with your mathematic explanations. Thank you sir. You are not only a big help but a big inspiration.

[@DrPhysicsA]

Think of a spring with a mass M oscillating up and down. When the mass reaches its lowest point it stops going down and starts going up. At that point its velocity is zero. But the spring has its maximum extension at that point. For a spring the force acting on the mass is F = Kx (where k is the spring constant and x is the displacement from the mid point). Since x is maximum at this point, so will be the force. But F = Ma so the acceleration is also maximum.

[@MrRasco97]

This is extremely helpful and I now fully understand but I wish they didn't have to call it simple haha

[@nedelser7233]

2:36 Me in most lessons

[@amrinahmed2279]

This is so accurate

[@DrPhysicsA]

Yes. You use the cos term if t=0 is when the pendulum/spring is at its maximum displacement from the mid point. You use the sin term if t=0 is when the pendulum/spring is at the mid point. y is the displacement from the mid point in each case. Just try values of t=0 in each formula and see what different values you get for y.

[@DrPhysicsA]

The playlist is in the most logical order that I could get it. I start with all the videos which relate to classical mechanics and then begin to move on to the concept of wave mechanics before going on to other aspects of physics.

[@lindadada-dadadal9864]

Everyone doing alevel physics needs to see this video! I am quite good at maths but smh used to puzzle me...not any more! Thank you soooo much sir!

[@Kundaikeith]

Indeed very helpful ,have been using this tutorial since Advanced Level Physics Class until now in my Engineering Physics Class........DrPhysicsA is a star

[@DrPhysicsA]

A guitar string oscillates as a standing wave. This means that its fundamental vibration will result in the middle of the guitar string having a much larger displacement than near the end. So the velocity of the oscillating guitar string in the middle will be greater than that at the end.

[@DrPhysicsA]

Yes. As the spring/pendulum oscillates it is exchanging Kinetic and Potential Energy. When displacement = 0, PE = 0 and KE is max. Hence v = max.

[@DrPhysicsA]

The pendulum example only works with small angles because we make the assumption that Cos theta equals 1, which is true for very small angles but becomes an imprecise assumption as the angle increases.

[@poligon333]

Very good video, straight to the point , no disruptions , thanks.

[@comic4relief]

I am not English, and not taking a physics course, but enjoy your videos. I study math on my own.

[@DrPhysicsA]

Yes. Omega is the angular sweep per second.

[@DrPhysicsA]

Yes but when the angle Θ is very small (which is the condition for the pendulum to swing with SHM) the two are pretty much the same. All motion is in the left-right direction and the up-down motion is ignored. So T=mg to a very good approximation.

[@DrPhysicsA]

A pendulum doesn't have a spring in it (usually). The reason both a pendulum and a spring oscillate is that whenver they are displaced from the mean position there is a restoring force which is acting to restore to the mean position. In the case of a pendulum that force will be due to gravity. In the case of the a spring it is caused by the inherent nature of the spring.

[@samadrashid7988]

This video made it so easy. Thumbs up!

[@onkarkepkar3801]

beautiful explanation!!! helped me in my exams......

[@toofresh91]

Total Mechanical Energy must be constant, through out the wave motion. At the crest, the PE will be at a maximum and KE at zero. Vice versa at the trough. E=PE+KE OR E=PE+(-KE)

[@skhoosy]

if we are considering a particle travelling through some sine curve y=sinx, how have you gotten to the conclusion that it would be defined by y=sinwt?

[@owensande]

I suggest watching at x1.25

[@EliteHalo5]

sounds like an asmr video

[@inthebackwiththerabbish]

rickmcn1986 weird

[@thomasgoodey1570]

doing gcses at the moment and i found this so helpful preparing myself for a levels as i am doing further maths, maths, physics and chemistry thanks again

[@afshinzaman2651]

How did it go

[@sraynambal870]

Hi, I'm confused why F=Ma= -TSin(Theta) , just confused with the negative sign.

[@DrPhysicsA]

Because its a restoring force i.e. it operates in the opposite direction to the displacement (whether measured by x or theta).

[@adn17]

Thank you sir.Very instructive and interesting. Simple to understand!

[@anupamac2151]

great vdeo . nice to c all topics stacked in 9 mins

[@SuperCricket777]

Strictly, when you define SHM, you get the equation 1) a = -(2piF)^2 x (taking 2piF as the constant, the angular frequency) But deriving this equation from the second derivative of displacement gives a = - A(2piF)^2 To account for the Amplitude in 1) is it correct to take the constant as A(2pif)^2 instead? Thanks

[@sushmitamondal962]

so useful... and u have actually cleared my basics concepts

[@comprehensiveboy]

Is omega the circular distance the particle moves in a second in radians? So.2*pi is one circuit so times that by the frequency and you get how many times it goes around in a second. But a radian is an angle size so getting a trig value of this for the y direction displacment is always gonna be between 1 and -1 which represents the amplitude without an A component?

[@joeradomski567]

My brain hurts

[@CorretorAlyssonGomes]

Your brain may not be ready.

[@profilename100]

great video but in edexcel physics you use it all the other way around as you start the oscillation at a max like in the cos graph so v is in sin and a is in cos

[@philipchristiansen1495]

At 5.32, how do you get w*sqrt(A^2-y^2). Though it should be w*sqrt(A^2-y^2/y^2) no?

[@sedani2]

why is the velocity at a maximum when the displacement is zero?? is it because its kinetic energy is greater at that point?

[@joemason31]

could you say that Acceleration of a spring can be written as -(2*pi*f)^2*x when f = frequency and x = displacement ???

[@DrPhysicsA]

Joe mason Yes because w = 2*pi*f

[@gertwallen]

Hi, when you are referring to the restoring force at 7:55, shouldn't the restoring force be tangent to the arc described by the pendulum motion due to gravity, i.e., mgsinΘ and not TsinΘ as you mention in the video? Thanks

[@NaraAIApp]

What? You can do that 😂..now im amaze..(the derivaation part)

[@sedani2]

thank you DrPhysicsA!! Im starting to get the hang of SHM now. Just one quick question if you dont mind? Is a pendulum oscillating because of the tension in the spring causing to contract when it reaches a certain amount and the force of gravity acting on it causes this process to continuously repeat? hope im making sense :P

[@zeckem8340]

a great summary of SHM. thanks a lot!

[@alen7648]

I think I‘ll give this video a chance.... looks good so far.....

[@turicaederynmab5343]

I went from learning about Friction too the oscillation of particles relative too harmonic motion? I think the playlist is a bit messed up...

[@SpaceOutlaww]

There is a minor mathematical error at the end of the video. The acceleration of the pendulum should be -gx/L instead of gx/L.

[@DrPhysicsA]

Arthur Johnson Correct. The force and acceleration are always in the opposite direction to the displacement. I was calculating the magnitude.

[@AlchemistOfNirnroot]

+DrPhysicsA Hence the annotation?

[@therealmaveric]

Brilliant video, it really helps with my a levels .

[@karishmamohun2473]

that is exactly what I was looking for thank you sir

[@PrimeEpoch]

At about 8:10, I don't see how you get that t sin theta is the only restoring force, since the mass also has to move downwards to get to the equilibrium position. This also, by logic, means that your 2nd equation must be wrong. Also, the weight is constant whereas the vertical component of tension varies with theta, so this is true only for a certain value of theta, but since the mass is in motion, the equation can't hold. Hope this helps :)

[@PrimeEpoch]

Ignore the first part, I misunderstood for a minute. I'm pretty sure that the 2nd equation doesn't hold though.

[@DrPhysicsA]

Kristen R You are right that the restoring force will vary with theta - thats how we get the SHM. The force, hence the acceleration, varies with displacement (which depends on theta).

[@andykopfleck]

Hi, Dr.Physics. How would you derive the Time Period of a Pendulum using F=ma & W=mg? Thank you for your attention.

[@DrPhysicsA]

Its included in many A2 level courses.

[@surry99]

what type camera an microphone do you use?

[@DrPhysicsA]

Just an ordinary digital camera with built in microphone.

[@ShadowZZZ]

at 5:28 how do you get to dy/dt = w*(A^2-Y^2)^1/2 ?

[@CrestinaBerzentho]

Sometimes we start with y=Acos(wt) except for y=Asin(wt) is there a difference ? a yes or No answer will suffice.

[@arielkatzir9126]

The way he says ''what is happening'' at 2:36 ...

[@anbtebist5961]

HI DRPHYSICS, why are you multiplying y= sinWT by omega (w) when you derive it?

[@SilverArro]

Chain rule

[@TheVashJa]

+Anbesa Teame Differential of the inner nested function in respect to its dependent variable multiplied by the differential of the outer function in repect to the inner nested function.

[@alwaysdisputin9930]

In DrPhysicsA's video "What is Light?" kzbin.info/www/bejne/q2LEaHetoK1qd8U he starts with an equation: Ψ = sin (kx - ωt) & then he differentiates in 2 different ways like this: ̲dΨ̲ = k cos ( kx - ωt ) dx ̲dΨ̲ = -ω cos ( kx - ωt ) dt So the letter that you put on the front depends on whether you say: dx or: dt

[@jointcc2]

why is omega square k/m

[@Sayeedur123]

Using a=-w^2 x

[@Mugetsuism]

Huh. Dy/Dt was never explained to us when we did SHM last month. It was simply: As the max and min values of sin and cos are 1 and -1 respectively, v = -wAsin(wt) and a = -w^2Acos(wt) simply become: v.max = wA and a.max = w^2A. Iv'e done AS maths and doing A2 now, but haven't differentiated cos/sin/tan so I didn't know how e was doing that (it looks like multiply by w and sin becomes cos, and cos becomes -sin). We're starting Chapter 8 Differentiation (last chapter) in C3 next week so I guess we'll learn that then?

[@TheLaprasMan]

d/dx cos(x) = -sin(x) d/dx sin(x) = cos(x) where y is the displacement of the particle: y=Asin(ωT) to find dy/dT which will give us the velocity we need to use the concepts above and the chain rule: The chain rule is used to find the derivative of two composite functions. Let's say y=f(g(x)), let's set g(x) to equal a variable to simplify things: z=g(x) (This is all the output of a function is: a variable) Then we have y=f(z) - much simpler. Let's take dy/dz=f '(z) we know z=g(x), so dz/dx=g'(x) now to cancel out dz we multiply dy/dz by dz/dx to find dy/dx: dy/dx = f '(z)*g'(x) z=g(x): dy/dx = f '(g(x)) * g(x)

[@ZyNeEnZyNe]

Ben Towers Thank you for taking the time to write that.

[@Mugetsuism]

Ben Towers I must have missed the notification in regards to your comment earlier; Just saw it now! Yep, we've finished doing the derivatives of trigs e.t.c. I really appreciate you taking the time to explain all of this. Iv'e finished with both SHM and Differentiation (chain/quotient rule e.t.c.) but never thought about using them together lol. I wish they integrated more maths into the physics course, but I guess those who aren't doing maths as-well will just lose their minds XD

[@AlchemistOfNirnroot]

+Asfandyar Khan A bit late but what he hell :P Someone in my class doesn't do A Level Maths. We just started Capacitance, when we started doing exponential relationships (i.e Q=Qe^-(t/RC)) she was baffled, the integral calculus for the coursework is going to be hell for her :D

[@yogithamanu7831]

Asfandyar Khan up HD h kg h

[@hunnybean269]

Shouldn't horizontal be cos and vertical be sin?

[@thenerdpoint5492]

No, the component through the angle is always cos and the one away from the angle is always sin. What he did is correct.

[@natureandchange]

why is the acceleration 0 at point B??. 3:12

[@PR0Z0MBIE9877]

Are you still interested in the answer? Acceleration in terms of SHM takes the form of a -sin(theta) wave. This means the value for acceleration will always be opposite to the displacement. At point B where displacement is 0, acceleration is opposite which also makes it 0. e.g. if displacement is -1, acceleration will be +1 (when looking at the two sine graphs).

[@JrYong]

Wow it doesn't seem so mind racking anymore, thanks for putting the simple in simple harmonic motion HaHa...

[@ahmadislam2364]

why it is not f=-ma? why it is positive? as acceleration is vector, acceleration should be negative, right?

[@Cobenis_Kar]

+ahmad zahir It is taken generally as a convention that, down or in the direction of gravitational acceleration, the sign is positive and that up or against gravity is negative. You can do it your way but, it will be more difficult. It has been made that way to make it more easier to do calculations.

[@PR0Z0MBIE9877]

Because for this equation we are not looking at gravity. Simply, the acceleration of the pendulum. a can be resolved into it's component vectors which will then directly be looking at gravity. But the a in the example in the video is solely looking at the resultant acceleration.

[@gertwallen]

right, T=mgcosΘ, so when Θ

[@Crehan.]

At 6:50, how did you derive that K/m is equal to omega?

[@DrPhysicsA]

Alfie Crehan I had previously shown that the general condition for SHM is a=-w^2 x So in this case k/m must be w^2

[@jamieshelley6079]

also can i ask, when you said maximum velocity at the point of 0 displacement, does this mean the velocity changes like this with other examples e.g a guitar, Having trouble visualising that for some reason. p.s thx for explaining the formulae in this clear manner

[@wangliz7208]

Why does F=ma=-T sinθ (in the pendulum question)?

[@DrPhysicsA]

+Wang Liz (Ludwig) When the pendulum is at an angle theta (and provided this is not more than a few degrees), the restoring force F=ma is provided by the component of the tension in the string.

[@PerspectiveX2]

+DrPhysicsA why does F=ma= minus Tsin(theta) and not positive Tsin(theta). Don't both the restoring force and the horizontal component of the tension act in the same direction?

[@DrPhysicsA]

+Saku Yes. But they angle is measured in the opposite direction to the restoring force hence the - sign.

[@waltermaths]

thank you, thank you, thank you

[@indikabatagoda94]

you are the best Drphysics :D

[@calteckk]

9:00 how does sin(theta) = x/L ?

[@suprimghimire4351]

very good explanation

[@internetuser9315]

Sir, how to know if a given equation represents a SHM or just a periodic motion???? pls help!!!!!!

[@arturopena3765]

force proportional to displacement and in the opposite direction...an example hook's law...F= -kx.....bigger displacement X,,,,,,, bigger restoring force F..... but in opposite direction.....

[@omirza7781]

I have created 2 playlists for A-level Physics for Edexcel, they are Paper 1 and Paper 2 make sure to check them out.

[@sedani2]

ok thanks a lot, i kind off get how these systems work now

[@CrestinaBerzentho]

Thank You, The explanation helped a lot.

[@yumenoritsu]

Nice, thanks so much!!

[@9point99poundsonly]

this is in fact as level. I have SHM in my unit 2 physics module.

[@xeryan2747]

sir, i dont understand why w=(k/m)^1/2

[@DrPhysicsA]

+Ting Tiew Yik We establish first that SHM occurs when a is related to x by the constant -w^2. Then when we find a relation for a spring that a=-kx/m we can deduce that k/m is w^2.

[@jokerman9295]

So omega=angular speed right?

[@marcushill2544]

Yes fam

[@DrPhysicsA]

Well actually its a frequency term. w = 2 pi f Frequency is number of cycles per second. w is no of radians per second.

[@surry99]

Thank you.

[@greghudson647]

why does F=-kx? Isn't Hookes law F=kx

[@DrPhysicsA]

That is in essence what I do at 08:20.

[@maniac8692]

awesome dude

[@SamsherSinghJoon]

i want A1 Level

[@AlchemistOfNirnroot]

AS?

[@hassanahmad3291]

there isn't a simple harmonic motion chapter in AS Level physics

[@dr.najeebullahqadir5858]

download a copy of the 9702 syllabus and see what topics are listed in As prepare accordingly

[@ninad0308]

is this for A2 CIE? OR AS?

[@DrPhysicsA]

N vhgmghhk Not sure. I prepare vids to cover AS and A2 level for AQA, OCR, Edexcel and CIE but not too sure how each board splits its AS and A2 work.

[@yousseftarkhan9210]

This is A2 in Cie

[@Nyuum]

ow meh gah

[@mukundjha792]

sir how to calculate epoch

[@DeMakAtak]

this helps.thanks

[@dk0r51]

06:19 "mid-position" = rest length

[@marystown23]

nice video :)

[@17sahilkumar]

Thank you sir

[@jamieshelley6079]

could you perhaps tell me why it only works with small angels, or buy that did you simply mean less than 90 (cos sin 09 - 1- seems that won't work)..idk if I answer my own question here :d

[@FaxandProbed]

This was a very good video.

[@asmacomidy7147]

mrc

[@masoodkhan857]

nice

[@arshahuja8490]

You sound like Richard Dawkins

[@andrewh996]

Is this a level? Because ive never seen this in my life

[@cilva7able]

HELP! I have a question and anybody feel free to answer. I'm confused about "frequency" and "w". What's the difference? Can you explain how T=1/f but when I'm doing sinusoidal modeling T=2pi/f.

[@Faste13]

T is how long per ONE cycle, f is how many cycles per ONE second therefore Txf = 1 in a way. what's sinusoidal modelling?

[@DrPhysicsA]

w - or omega - is the frequency in radians per second. f is the frequency in cycles per second. Since there are 2 pi radians in one complete circle (cycle) w = 2 pi f.

[@RedzyOne]

Nice¬¬¬¬¬

[@linkchibi]

so difficult -.-

[@clotanoob]

It is so blur...

[@jamieshelley6079]

I'd been expecting something well ..more challenging for A2,not sure if I'm going to like the following year or get annoyed at examiners simplifying to the extend you have to learn how to simplify your own studies to tick the boxes so to speak. anyone got experience in this ?

[@azerverycarry3879]

COMES HERE BECAUSE YOU HAVE HOMEWORK OF MECHANISM OF MACHINES