Diff between Simple Harmonic Motion and Harmonic Motion?

[unsung]

---

Members don't see this ad.

So, this is a Q from EK:

Which of the following is NOT simple harmonic motion?

A. An electron moving back & forth in ac current.
B. The orbit of the earth around the sun as viewed from the side.
C. A pendulum swinging at a small angle.
D. A boy bouncing a yoyo in a steady rhythm.

The answer is D, and the explanation was that while a yoyo's movements constitute "harmonic motion", it was not simple harmonic motion. The other examples are all simple harmonic motion, and their definition for simple harmonic motion was any motion that can be described by a sine function.

Okay, that's fine. But, another question asks:

Which of the following waves can NOT be represented by superimposing sine wave functions?

A. The crying of an infant
B. A square wave
C. Any motion whatsoever
D. All of the above can be represented by an infinite number of superimposed wave functions

So, the answer is D. Which kind of confused me. So if "any motion whatsover" can be represented by some set of sine wave functions, how come simple harmonic motion is definted as just any motion that can be described by the sine function?

 

[Kaustikos]

Are you sure that's exactly what it said? For the definitino and the choices? I would've chosen C outright because any answer with "Any", or "All" or "never" is usually wrong.

Not to mentoin it conflicts with your previous question. Unless there is something missing. I figured that the simple harmonics was not applicable to the yo-yo for a completely different reason; oh well.

Any motion whatsoever?

edit - that question CAN'T be right.

 

[tncekm]

I think that question # 2 is mean to stress the point of wave summation.

If you were to add enough sine waves together you could probably get almost any wave form.

I'm not sure if I would have gotten that question right if I hadn't seen the answer first, but I personally think that the answer is legitimate.

Note: Question #1 doesn't have much to do with Question #2 because, as the thread title implies, question #1 is referencing only simple harmonic motion.

 

[phospho]

I think that question # 2 is mean to stress the point of wave summation.

If you were to add enough sine waves together you could probably get almost any wave form.

I'm not sure if I would have gotten that question right if I hadn't seen the answer first, but I personally think that the answer is legitimate.

Note: Question #1 doesn't have much to do with Question #2 because, as the thread title implies, question #1 is referencing only simple harmonic motion.

I agree. I also don't see any commonalities between the two, at least nothing that would have helped in solving them.

Also, I remember reading in EK physics somewhere that if given the right waves, we can make ANY wave form. They emphasized "any". That's why I agree with tncekm in assuming that the 2nd question is trying to stress "any". Don't worry about what each option means. Just focus on the fact that it's everything.

 

[Kaustikos]

I think that question # 2 is mean to stress the point of wave summation.

If you were to add enough sine waves together you could probably get almost any wave form.

I'm not sure if I would have gotten that question right if I hadn't seen the answer first, but I personally think that the answer is legitimate.

Note: Question #1 doesn't have much to do with Question #2 because, as the thread title implies, question #1 is referencing only simple harmonic motion.

I misinterpreted the two. That's right.

 

[physics junkie]

So, this is a Q from EK:

Which of the following is NOT simple harmonic motion?

A. An electron moving back & forth in ac current.
B. The orbit of the earth around the sun as viewed from the side.
C. A pendulum swinging at a small angle.
D. A boy bouncing a yoyo in a steady rhythm.

The answer is D, and the explanation was that while a yoyo's movements constitute "harmonic motion", it was not simple harmonic motion. The other examples are all simple harmonic motion, and their definition for simple harmonic motion was any motion that can be described by a sine function.

Okay, that's fine. But, another question asks:

Which of the following waves can NOT be represented by superimposing sine wave functions?

A. The crying of an infant
B. A square wave
C. Any motion whatsoever
D. All of the above can be represented by an infinite number of superimposed wave functions

So, the answer is D. Which kind of confused me. So if "any motion whatsover" can be represented by some set of sine wave functions, how come simple harmonic motion is definted as just any motion that can be described by the sine function?

Question #2 is kind of funky. If you look up what a fourier series is(no one expects you to be able to do them but it doesn't take much work if you've had calc 2) then you will see that this is actually a very widely used thing in mathematics. It turns out all functions that fit certain requirements can be expressed as a combination of sine waves. Even a square wave or a triangle wave. This is engineering/physics math though and I'm not sure what the EK writer was smoking when he decided to toss this question in.

Question #1

Wikipedia says "Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals[very important part] in a specific manner - described as being sinusoidal, with constant amplitude."

Now you see the criteria which isn't met by your yoyo is that it is damped and driven. Damped just means there is some kind of resistance that will eventually slow the process to a halt if nothing does work on it to keep it going. Driven just means you are continuously exerting force on the system to keep it oscillating. Frankly none of these are perfect harmonic oscillators but the yoyo sticks out because the system, if you let it alone, would stop immediately. The grandfather clock would ideally keep swinging assuming no friction, the planets will keep going around the sun, and an electron will keep moving back and forth in an AC field. The yoyo, however, is not oscillating as casually as the others. You have to do work on it to get it to change so its motion isn't periodic in any kind of ideal setting like no friction, etc.

 

[unsung]

Question #2 is kind of funky. If you look up what a fourier series is(no one expects you to be able to do them but it doesn't take much work if you've had calc 2) then you will see that this is actually a very widely used thing in mathematics. It turns out all functions that fit certain requirements can be expressed as a combination of sine waves. Even a square wave or a triangle wave. This is engineering/physics math though and I'm not sure what the EK writer was smoking when he decided to toss this question in.

That's pretty cool. Thanks!

Question #1

Wikipedia says "Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals[very important part] in a specific manner - described as being sinusoidal, with constant amplitude."

Now you see the criteria which isn't met by your yoyo is that it is damped and driven. Damped just means there is some kind of resistance that will eventually slow the process to a halt if nothing does work on it to keep it going. Driven just means you are continuously exerting force on the system to keep it oscillating. Frankly none of these are perfect harmonic oscillators but the yoyo sticks out because the system, if you let it alone, would stop immediately. The grandfather clock would ideally keep swinging assuming no friction, the planets will keep going around the sun, and an electron will keep moving back and forth in an AC field. The yoyo, however, is not oscillating as casually as the others. You have to do work on it to get it to change so its motion isn't periodic in any kind of ideal setting like no friction, etc.

Wow, I never drew the connection betw SHM & damping/driving. That makes sense now. You're awesome 👍

 

[SSerenity]

Question #2 is kind of funky. If you look up what a fourier series is(no one expects you to be able to do them but it doesn't take much work if you've had calc 2) then you will see that this is actually a very widely used thing in mathematics. It turns out all functions that fit certain requirements can be expressed as a combination of sine waves. Even a square wave or a triangle wave. This is engineering/physics math though and I'm not sure what the EK writer was smoking when he decided to toss this question in.

Question #1

Wikipedia says "Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals[very important part] in a specific manner - described as being sinusoidal, with constant amplitude."

Now you see the criteria which isn't met by your yoyo is that it is damped and driven. Damped just means there is some kind of resistance that will eventually slow the process to a halt if nothing does work on it to keep it going. Driven just means you are continuously exerting force on the system to keep it oscillating. Frankly none of these are perfect harmonic oscillators but the yoyo sticks out because the system, if you let it alone, would stop immediately. The grandfather clock would ideally keep swinging assuming no friction, the planets will keep going around the sun, and an electron will keep moving back and forth in an AC field. The yoyo, however, is not oscillating as casually as the others. You have to do work on it to get it to change so its motion isn't periodic in any kind of ideal setting like no friction, etc.

I realize its 2013, but this question still confuses me. Why do we assume the yoyo is dampened and not the pendulum? We have no way of knowing this pendulum belongs to a grandfather clock.

 

[The_Sunny_Doc]

I realize its 2013, but this question still confuses me. Why do we assume the yoyo is dampened and not the pendulum? We have no way of knowing this pendulum belongs to a grandfather clock.

"A pendulum swinging at a small angle." That's the key phrase. Only a pendulum swinging at a small angle would satisfy the requirements for SHM. One of the requirements for SHM is that the restoring force is proportional to the object's displacement from equilibrium, with the force directed towards that equilibrium position. Think of the restoring force acting on a spring and Hooke's Law.

F= -kx

Since the angle is the measurement of displacement for a pendulum (how big of a piece of pie does its trajectory make??), you can sub theta for x Hooke's law when working with pendulums.

F= -kθ

What force causes a pendulum to be "restored" to its original position, which is hanging straight down? Gravity. So we sub mg for k. K is only used for springs, being a measure of how much force the metal coil will apply to "restore" the object on the spring.

F=-mgθ

This only works when theta is small because the force vector pushing the bob back down to equilibrium is actually equal to mgsinθ, not mgθ. See the pale fuschia vector in the pic below. I filled in the similar angles with purple using mspaint. The original pic is from a website so I don't take credit for it.

So you can see how at small angles of displacement from the equilibrium, you can set the restoring force (that vector "pulling" the pendulum bob back to the center) equal to mgθ instead of mgsinθ. If the pendulum swings out at an angle greater than about 30 deg you couldn't use that approximation and SHM would no longer describe the pendulum.