How Does Doubling the Amplitude Affect the Oscillation Period?

[1MileCrash]

Homework Statement

A weight suspended from an ideal spring oscillates up and down. If the amplitude of the oscillation is doubled, the period will

Homework Equations

The Attempt at a Solution

There are no equations relating xm to T. Obviously it gets larger, but how do I find the factor, magic?

 

[PeterO]

Homework Statement

A weight suspended from an ideal spring oscillates up and down. If the amplitude of the oscillation is doubled, the period will

Homework Equations

The Attempt at a Solution

There are no equations relating xm to T. Obviously it gets larger, but how do I find the factor, magic?

There is good reason why there are no formulas/equations relating amplitude to period!

 

[1MileCrash]

Well, can't exactly tell my homework that.

Obviously they are related in some way - angular frequency constant. But it's not in my book.

 

[PeterO]

Well, can't exactly tell my homework that.

Obviously they are related in some way - angular frequency constant. But it's not in my book.

What do you mean by angular frequency? This is a mass moving vertically on the end of a spring?

 

[1MileCrash]

Simple harmonic motion has angular frequency...

Anyways, could I have some help solving this problem?

 

[therealnihl]

Unless we are misunderstanding the question, what PeterO is implying by "good reason" is since there is no equation relating period and amplitude, changing the amplitude has no effect on the period or the angular frequency. You intuition that doubling the amplitude has to have some effect is wrong.

 

[PeterO]

Unless we are misunderstanding the question, what PeterO is implying by "good reason" is since there is no equation relating period and amplitude, changing the amplitude has no effect on the period or the angular frequency. You intuition that doubling the amplitude has to have some effect is wrong.

Indeed. With larger amplitude we have larger speeds involved, but that is essential since the mass has to cover a greater distance in the same time.

If amplitude was a factor, clock makers would have to be very inventive to check the pendulum had just the right amplitude.

 

[1MileCrash]

Unless we are misunderstanding the question, what PeterO is implying by "good reason" is since there is no equation relating period and amplitude, changing the amplitude has no effect on the period or the angular frequency. You intuition that doubling the amplitude has to have some effect is wrong.

That makes sense, thanks for the help therealnihl. I don't have the time to be jerked around for 4 hours.

 

[PeterO]

That makes sense, thanks for the help therealnihl. I don't have the time to be jerked around for 4 hours.

And so eloquently stated by someone unwilling to google "amplitude and simple harmonic motion".
And get the first response from a wikipedia reference.

"These equations demonstrate that the simple harmonic motion is isochronous (the period and frequency are independent of the amplitude and the initial phase .."

You didn't even have to got to, and read, the wikipedia entry.

Having to wait 4 hours to be told the answer must have been difficult. You could have read your text - or googled - while you waited.

This site is not for being spoon fed an answer - indeed it is forbidden to simply provide an answer - it is for seeking reference/guidance to the answer.

 

[therealnihl]

For the record, I think PeterO's response was way better than my own; since he explained the physical reason as to why amplitude is not related to frequency/period/angular frequency. Which is the whole point of learning physics (to gain a physical intuition rather than merely look for equations in the book/forums).

 

[1MileCrash]

And so eloquently stated by someone unwilling to google "amplitude and simple harmonic motion".
And get the first response from a wikipedia reference.

"These equations demonstrate that the simple harmonic motion is isochronous (the period and frequency are independent of the amplitude and the initial phase .."

You didn't even have to got to, and read, the wikipedia entry.

Having to wait 4 hours to be told the answer must have been difficult. You could have read your text - or googled - while you waited.

This site is not for being spoon fed an answer - indeed it is forbidden to simply provide an answer - it is for seeking reference/guidance to the answer.

I don't need to be spoonfed or told the answer, but asking facetious questions followed by three question marks? are not helpful.

 

[PeterO]

I don't need to be spoonfed or told the answer, but asking facetious questions followed by three question marks? are not helpful.

Given the number of people who mis-post while they are doing many problems at the same time, I wondered if you were mixing up a mass moving vertically on a spring with some object traveling in a circle.

I have never seen the term "angular frequency" before, and have analysed shm for masses on springs on many occasions.

Oh, and in this problem, you did need to be spoonfed, and told the answer.

 

[1MileCrash]

Oh, and in this problem, you did need to be spoonfed, and told the answer.

Nope, just happened to happen before any real advice or insight was given.

Might I suggest an example approach such as:

"Think about this, if the amplitude is increased, what is the velocity at the points past the old amplitude comparatively?" or some other questions to, like, jog someone into thinking. That's the point. You've got to be crazy if you think telling me:

"What do you mean by angular frequency? This is a mass moving vertically on the end of a spring?"

"There is good reason why there are no formulas/equations relating amplitude to period!"

Is anything helpful.

So please, by all means, don't tell people the answer, but tell them something to make them think. Your responses are along the lines of "I know the answer and why, sucks that you don't bro."

 

[cepheid]

Nope, just happened to happen before any real advice or insight was given.

Might I suggest an example approach such as:

"Think about this, if the amplitude is increased, what is the velocity at the points past the old amplitude comparatively?" or some other questions to, like, jog someone into thinking. That's the point. You've got to be crazy if you think telling me:
Is anything helpful.

So please, by all means, don't tell people the answer, but tell them something to make them think. Your responses are along the lines of "I know the answer and why, sucks that you don't bro."

You presumably already knew that ω = √(k/m) for a spring, which means that ω only depends on k and m. There is no dependence on the amplitude. Therefore, PeterO's hint was actually a good one. What he was saying was: "There is a good reason why there are no equations relating the period to the amplitude: it's because the period and the amplitude are independent of each other, as shown by the equation for the period, which doesn't include the amplitude." He didn't say the part in italics, because you were meant to fill that in yourself. That's why it's called a hint...a hint designed to make you go back and take a closer look at what the equation said.

EDIT: I also don't think PeterO was being facetious at all with the three-question mark questions. I think he was just genuinely seeking clarification on what you said in post #3.

Furthermore, when I learned SHM, it was defined as a periodic/oscillatory motion in which the period is independent of the amplitude. As others have already pointed out, a very short time on Google (much less than 4 hours) would have revealed this if you had made the effort to look into it. I would advise you strongly to lose the attitude. EDIT:I would advise that because people on this site are doing you a favour by giving generously of their limited time to help you learn physics. Nobody is obligated to do anything for you at all, let alone provide help that specifically meets your (unreasonable) standards for what is "useful."

 

[1MileCrash]

My standards are not unreasonable, they are met and exceeded in almost every topic. That is, a "mental nudge" towards the next step in really grasping, and several more if necessary.

I didn't display any attitude first. Having questions thrown back at me like I was stupid. PeterO's first couple of posts only frustrated me, and pissed me off, and I mean badly. From a meaningless statement to a nitpick of semantics and terms, you can't tell me that in my position, you would have exclaimed "eureka!" So, now I'm upset again. I understand the appeal of arbitrarily taking the side of someone who takes time out of his free time to help others, but that doesn't make his methods unassailable.

And lastly, it looks strange that I am accused of wanting to be told the answer (I don't) and in the same breath I am told to look the answer up on google rather than have a discussion with someone (emphasis on discussion) that can guide me into understanding. No, I didn't sit at my computer for 4 hours, I moved on to new material.

So, if I sound like I have an attitude, it is because I came here seeking guidance, and had questions thrown back at me like I was freaking retarded.