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### Course: Physics archive>Unit 8

Lesson 2: Simple harmonic motion (with calculus)

# Introduction to harmonic motion

Harmonic motion refers to the motion an oscillating mass experiences when the restoring force is proportional to the ​displacement, but in opposite directions. Harmonic motion is periodic and can be represented by a sine wave with constant frequency and amplitude. An example of this is a weight bouncing on a spring. Created by Sal Khan.

## Want to join the conversation?

• Why is Sal so emphasizing on the toughness of Calculus?
Is it really important to learn Calculus to understand Physics?
I just managed to pass my Math exams in 10th grade and now having left Maths(opted for Biotechnology instead) in 11th, am now unable to understand what is this Calculus all about?:/:/:/
How can a student who has not understood basic concepts of Algebra study this stuff?:'(
Pls. help with any suggestions:(
• Sal is not emphasizing that calculus is tough so much as he is avoiding the use of calculus for the sake of not confusing people who don't understand it. Physics is the study of the way the world actually works. As such it is important for anyone to have a good intuitive understanding of physics whether or not they are good at math. That is why Sal avoids discussing the calculus whenever it is not necessary to the discussion. That said, solving physics problems of this sort is what motivated Issac Newton to invent calculus in the first place. Newton made all kinds of experimental observations of motion, but he didn't have the mathematical tools to describe what he was seeing. (At that point, a rudimentary understanding of algebra was all that Newton had and that was self-taught.) Newton took a break from his physics experiments, and scrutinized his results. This led him to develop tables of what we now know as derivatives. (Keep in mind that Newton was inventing this math on the fly so the notation that we have today didn't exist yet.) Newton also noticed that for each derivative there was a corresponding sum from which the derivative could be obtained. This led to the concept of what we now know as an integral. The physics that we're trying to learn in these videos was the motivation for the invention of calculus. Calculus is all about motion. The final answer to your question is that you don't have to know calculus to learn physics but it helps ... it helps a lot.
• How come the spring has the highest velocity, or most kinetic energy, at the point 0? Do all springs always have their highest velocity at the halfway point?
• Point 0 is called the equilibrium point. So if you imagine a spring just sitting there, that's point 0. If you attach that mass and let gravity pull it down, that's A, and A has a lot of potential energy because the spring is going to want to bounce back. The spring will bounce back past 0 (where it's moving the fastest and has maximum kinetic energy) because of its restorative force (how "springy" the spring is). It will then compress to -A, where it's got high potential energy (because if you compress a spring, it's going to bounce back.)
Basically, the spring wants to be at 0 because that's equilibrium, and the restorative force is always trying to get to equilibrium, but it can't.
The answer to your second question is yes. That's a fundamental property of simple harmonic motion (pendulums, too) and it will come up all the time.
• what is damped oscillation and resonance?
• A spring and mass together make an oscillator. Add friction, and you have a damped oscillator, where the oscillations decrease over time.

Every oscillator has some natural frequency at which it wants to oscillate. If you give it an extra push at that frequency, you will get much bigger oscillations. That's resonance.
• in what does the formula next to the diagram mean?
F=Kx,and X(t)=?
also does Cos stand for the cosine
• The force applied by a spring on a mass is given by the model F_spring = –kx. "k" is called the spring constant and it is a measure of the stiffness of the spring. "x" is the displacement of the spring from its equilibrium position. The negative sign indicate that the spring applies a force in the opposite direction of the displacement. "x(t)" is the displacement from equilibrium as a function of time. And "cos" is the cosine function.
• shouldn't the independant component be on the X axis?
so,time should be on the X axis,right?
i'm confused...am i missing something here?
• The spring does not rotate, so why does the formula use angular velocity(omega) in the cosine?
• Can someone explain how we know it's a cos function?
It could be some other function, where x(t)=1 at t=0, and x(t)=0, at x=1 and so on periodically, right?
• We here take it as a cos function because we don't know any other function that is periodic and shows such kinda behaviour.
(1 vote)
• What is the difference btwn mechanical and non mechanical oscillators?