Simple Harmonic Motion: Hooke’s Law

Professor Dave here, let’s discuss simple harmonic motion. Sometimes when we examine the motion of an object, it will involve a single action, like a rock falling from a cliff down to the ground. This will probably just happen one time after which the rock will remain at rest. But some motion is periodic, meaning repeated, like the motion of the pendulum on a grandfather clock, or the vibration of a spring. We will refer to this kind of motion as simple harmonic motion. Say we have a spring that is attached to some stationary surface, and on the other end of the spring there is a block of a particular mass. If we pull this block so as to expand the spring and then we release the block, it will vibrate back and forth between more compressed and less compressed states. If we assume that the surface of motion is completely frictionless, then the elastic potential energy reaches a maximum when the spring is most or least compressed and the block is changing direction, while kinetic energy is at a maximum when the block is right in the middle and moving the fastest. If we were to graph the position of the block against time it would display sinusoidal behavior, just like a trigonometric sine function, where the block continues to occupy the same positions over a particular period of time, which is why we call this periodic motion. x equals 0 at the equilibrium position of the block, where it was at before we pulled it, and assuming zero friction the block will oscillate between positive x and negative x indefinitely. In reality, frictional forces will dampen the spring’s activity and it will eventually come to a stop, but for many systems an ideal mass-spring system will be a decent approximation for a real one. Of course every spring is different, some are loose like a slinky and some are stiff like the spring that launches a pinball into play. This factor is represented by the spring constant k, which will be unique to a particular spring. The force that a spring can exert is equal to negative k times the displacement of the object it acts upon, and this relationship is called Hooke’s law. The negative sign indicates that the force of the spring is always opposite the direction of the movement of the object. When the object compresses the spring it will push out, and when the object stretches the spring it will pull in. In both cases, the spring is attempting to move the object back to its equilibrium position, which is why the force applied by the spring can be called a restoring force. The units on a spring constant will be Newtons per meter, so that when you multiply by some distance x, you get the force that must be applied to compress that spring that far. Let’s also note that the elastic potential energy of a spring will be equal to one-half kx squared, where k is the spring constant and x is the distance it is stretched or compressed. If at equilibrium the distance is zero, so it has zero elastic potential energy, and the maximum elastic potential energy will occur at the maximum distance from this point on either side of the oscillation. This expression looks similar to the expression for kinetic energy, which is convenient since the two will interchange as the mass oscillates. A pendulum also displays periodic motion since it swings back and forth between the same two positions, although this involves gravitational potential energy rather than elastic potential energy, and we will look at this behavior next. Let’s check comprehension. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me:

52 thoughts on “Simple Harmonic Motion: Hooke’s Law”

• Avegarohan Jaiswal Post author

being the first to comment I hope a reply form u professor !!!!

• Oh Boi Post author

I too need a reply from Dave!

• SailorJenova Post author

Sweet this makes it waaaaay easier to understand IR spectroscopy ….I swear, IR is just about the most difficult thing I have encountered that I have to go back constantly over every time I have to use it….I'm getting there, but it's annoying. Only 1-H and 13-C NMR is worse. Thanks Dave, you the MAN! (..^.^..)

• arpit arora Post author

prof….what will be ur next topic?

• Subhabrata Ghosh Post author

do you have any lectures on carbenes….. but i like your lectures…:):)

• Toxic Sunset Post author

hey thanks for making these videos! I am taking 2 physics courses over the summer so I will definitely be watching all of these (and liking and sharing links too lol)

• PVCmannen PVC4life Post author

Dave what is pvc for you, is it life ?

• Brandon Redmond Post author

1:19 Could you say it exhibits cosinusoidal behavior? What is the difference?

• STUDY & TRAVEL Post author

in the comprehension why did the force become negative ?

• Leila Aglan Post author

what is dave's full name ?

• Manuel Ignacio Balaguera Jiménez Post author

Excellent, thanks very much from Colombia.

• MLGFearlessGamer Post author

You have no idea how much you just helped me understand this subject. Thanks alot.

• Parveena begum Post author

Explain relationship between newton's third law of motion and reflection of light.

Or
Differentiate , in your next coming video

Plz plz plz plz
I hope you are honest professor .

• Sep M Post author

would Fspring always be negative value since by def its Fspring = -kx?. cause on the comprehension, when the spring is stretched, Fspring and spring constant were both negative resulting in positive distance which makes sense since the distance is getting stretched making the distance longer to the right from the equilibrium position.

But if we changed it to the spring being compressed. We can make Fspring positive value right? since +Fspring / -k will result into -x(distance) which makes sense also since the spring is being compressed down making the spring shorter away from the equilibrium to the left?

• MorningWoodChopped Post author

im not understanding that tbh, if compression is positive and stretching it is negative, then if you stretched it (negative direction) how did you get positive displacement (compression)? this is basically saying you stretched it from its resting place and some how it compressed .234 m. if youre describing stretching as negative then you would have stretched it -.234 m multiplied by -k and gotten a positive force, but in your equation you got a negative force, am i not getting this or what. the only way i got it to work out was to describe stretching as positive. that would give -k(.234)=-15.3n the reason the force is negative is because that is the force at which the spring is pulling back on you with. then the .234 makes sense to me because you stretching it didnt mean you compressed it somehow lol unless im completely wrong and am fucking brain dead

• Musab Qaiser Post author

How many times has he used this shirt

• StarClick Times Post author

Plz make all videos of class 12. We are your greatest fan. So we want to learn physics from you next session it is in class 12

• miaeba Post author

I really like the music at the end of the vids.

• S Semwal Post author

Please solve string theory's equation, in simple and easy way.
And also demonstrate how computer code (binary code) found in deeply solving the string theory. Reply first

• imran zakir Post author

thank you so much!!!! your videos help me a lot professor.

• Novalium Company Post author

He knows a lot about the science stuff, professor dave explains! This intro song is stuck into my head, help.

• A V Post author

Hi Prof Dave could you please explain to me as to why the force on the spring is negative?

• Sathyabama V Post author

Nice explanation

• uushonam Popyeni Post author

You are the best professor!!!!!

• Atchu K Post author

In which university u studied

great

• SHHHWIFTY Post author

Arigato Jesus sama

• Chilla Ndp Post author

Explain the chapter system of particles

• Jharna Ahuja Post author

You teach very well sir! Got it 💓

• BBC NEWS SOMALI TV Post author

thanks so much teacher, I have well unders

• Achinta Manna Post author

sir you are from which country

-65.6N/m/-15.3N = 4ish … what did I do wrong?

• Habiba Amro Post author

really thank you professor dave its being easy
from UAE

• varsha tak Post author

thank you sir

• Subramanyan R Post author

amazing content

• Jojo Super Post author

you are awesome sir. thank u

• iTooDear Post author

TANK YOU! I finaly understand this… Subed!

• HEY STOBH IT Post author

Oh my goodness I was stuck on this one physics question for a good 25 minutes so I took to the internet for help. I stumbled across your video and had a lightbulb moment at 3:28! Thank you so much because this video really helped :))

• Tahir Hussain Post author

What is the displacement of the object in SHM when the kinetic and potential energies are equal?

• binita kumari Post author

From india here…you explanation is absolutely awesome. I understand everything here thanks a lot professor Dave

• TheAlex0903 Post author

In which scenario do you know to use 1/2 kx^2 instead of -kx

• Elle Szabo Post author

dude has a nerdy tattoo bet

• Ocin Post author

why is he so happy in the intro and so sad in the video lmaooo

• Miguel Asuncion Post author

Thanks professor dave

• Mariam Mohamed Post author

Cause of this vidoe I understant my lesson , thanks very much about that you have like this explanation and share it 👌👌

• Nouran Kb Post author

you are a legend of explaining!

• Prakash Raj Post author

Why force is in negative

• _Nameless _ Post author

Wait does he wear the same shirt every time