Simple Harmonic Motion Oscillations

verd

Hi,

So I'm having a little bit of trouble answering a couple of simple questions regarding simple harmonic motion...

[Image]
All of this is regarding the really simple image ^

Oscillations are not always described by equations; you should also be able to analyze the graphical representation of motion. Answer the following questions related to the graph describing the oscillations of the block on a spring.

-Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time.

Easy enough, right?
Here are some answers I got that were correct:

Q: What is the period T of oscillations:
A: 0.02s
Q: How long a time t does the object take to travel from the point of maximum displacement to the opposite point of maximum displacement?
A: 0.01s
Q: An object passes the equilibrium position. What time t would elapse before it passes the equilibrium position again?
A: 0.01s

And here is the one I'm having trouble with:
Q: What distance d does the object cover during one period of oscillation?
...They want the answer in meters. ...But they seem to want a number, and all I can come up with is either 0, 2A, or A...

Because I don't have A, I'm not sure how to solve this-- and if I have to find A, I'm not quite sure how to do it...

Any pointers?

And for one other--

In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s.

Find the spring's force constant.

Okay, I know the formulas-- And I've attached an image of the interval of time they're talking about-- (It'd be the red part)
But would I be assuming, here, that gravity is slowing this one down? They say, 'In a physics lab'... ...So this wouldn't be an ideal system... But an ideal spring?

I've gotten a host of different numbers-- all of which are incorrect. Any ideas?

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OlderDan

Homework Helper
You are not showing us the graph referenced by the first problem. If you have a graph of x vs t, you should be able to read A from that graph.

For the second problem you can assume no friction and a horizontal track so gravity is not a factor. This is a simple matter of relating the period of motion to the mass and the spring constant. An ideal spring is one that can be both compressed and stretched with the same force constant for either. On an air track the equivalent situaiton is usually achieved by using two streched springs, one on either side of the glider.

verd

you're right-- I'm sorry. I linked you to the wrong image...

[Image]

OlderDan

Homework Helper
verd said:
you're right-- I'm sorry. I linked you to the wrong image...

[Image]
I still do not see any numbers. Do you have numbers to go with the letters?

verd

OlderDan said:
You are not showing us the graph referenced by the first problem. If you have a graph of x vs t, you should be able to read A from that graph.

For the second problem you can assume no friction and a horizontal track so gravity is not a factor. This is a simple matter of relating the period of motion to the mass and the spring constant. An ideal spring is one that can be both compressed and stretched with the same force constant for either. On an air track the equivalent situaiton is usually achieved by using two streched springs, one on either side of the glider.
Right, so I have the formula:

$$T=2\pi\sqrt{\displaystyle{\frac{m}{k}}}$$

However, I was given half a period-- as illustrated in that crude little diagram I drew up for you, heheh. Would I just then multiply the given time period by 2??

I understand that this is just a general plug-n-chug problem once you get the period-- but how do I know exactly what the period is? I would imagine that it's 2(2.60s)-- But when I solve for k, I end up with 0.292N/m... Which isn't correct, is it?

verd

OlderDan said:
I still do not see any numbers. Do you have numbers to go with the letters?
That was the image I was given-- so I'm equally as confused as you would be. ...In a 'hint', at one point, that was not a part of the question, I was given this:

"In moving from the point t=0 to the point K, what fraction of a full wavelength is covered? Call that fraction a. Then you can set $$aT=0.005\;\rm s$$. Dividing by the fraction a will give the period T."

So that's all I have-- and I have no idea as to how they expect me to come up with a number for the answer given only that. All I have is the period. To find distance, I'd need other quantities, wouldn't I? I thought that the answer might have been 0, assuming that the distance travelled was measured using positive and negative displacements, cancelling each other out... But I don't know what they expect me to do with this one...

OlderDan

Homework Helper
verd said:
Right, so I have the formula:

$$T=2\pi\sqrt{\displaystyle{\frac{m}{k}}}$$

However, I was given half a period-- as illustrated in that crude little diagram I drew up for you, heheh. Would I just then multiply the given time period by 2??

I understand that this is just a general plug-n-chug problem once you get the period-- but how do I know exactly what the period is? I would imagine that it's 2(2.60s)-- But when I solve for k, I end up with 0.292N/m... Which isn't correct, is it?
Looks right to me. I think you have done it perfectly.

OlderDan

Homework Helper
verd said:
That was the image I was given-- so I'm equally as confused as you would be. ...In a 'hint', at one point, that was not a part of the question, I was given this:

"In moving from the point t=0 to the point K, what fraction of a full wavelength is covered? Call that fraction a. Then you can set $$aT=0.005\;\rm s$$. Dividing by the fraction a will give the period T."

So that's all I have-- and I have no idea as to how they expect me to come up with a number for the answer given only that. All I have is the period. To find distance, I'd need other quantities, wouldn't I? I thought that the answer might have been 0, assuming that the distance travelled was measured using positive and negative displacements, cancelling each other out... But I don't know what they expect me to do with this one...
I can't see any connection to numbers, but in terms of the amplitude, A, the distance moved during one full cylce (not the net displacement of zero) would be 4A. From your diagram, A would be R or (1/2) (R - Q). Given values for those, or a way to calculate them would do it. I don't see where that time number comes from. Did they give you anything like maximum velocity or acceleration?

verd

I didn't get a value for anything... Aside from that weird hint in the middle of nowhere, this is all I got:

Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion.

Motion that repeats (or almost repeats) itself after a certain interval of time is called periodic motion. One can think of many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a heavy block suspended on a spring bouncing up and down.
The latter example differs from the first two. It represents a very special kind of periodic motion called simple harmonic motion, which is motion with oscillations or vibrations.

The conditions that lead to simple harmonic motion are as follows:

* There must be a position of stable equilibrium.
* There must be a restoring force acting on the oscillating object; the direction of such a force must always be toward the equilibrium, and the magnitude of that force must be directly proportional to the magnitude of deflection from the equilibrium. In other words, the restoring force $$F_vec$$ is given by $$\vec F=-k\vec x$$, where $$x_vec$$ is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.
* The resistive forces in the system must be reasonably small.

In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them.
Between that and the displacement question, there were a few questions asking me to find the frequency and period of a few different situations involving the first picture, and then I got this... EXACTLY (It goes with that second picture that I linked you to)

Oscillations are not always described by equations; you should also be able to analyze the graphical representation of motion. Answer the following questions related to the graph describing the oscillations of the block on a spring.

Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time.

Q:Which points on the x axis are located at a distance A from equilibrium?
A:both R and Q

Q: Suppose that the period of oscillations is T. Which points on the t axis are separated by the time interval T?
A: zero and N

Q: Suppose that the period of oscillations is T. Which points on the t axis are separated by the time interval T?
A: K and P

Q: What is the period T of oscillations?
A: 0.02s
[This is the question that I had to click the 'hint' button with, in order to obtain the weird value]

Q: How long a time t does the object take to travel from the point of maximum displacement to the opposite point of maximum displacement?
A:0.01s

Q:An object passes the equilibrium position. What time t would elapse before it passes the equilibrium position again?
A:0.01s
And this is where I'm stuck:

Q:What distance d does the object cover during one period of oscillation?

...The only numbers I have, is the period. Without other values, there is no way I can find the spring constant, is there?
I've already tried 4A, but when I enter the answer, I am told that A is not a part of the answer... And they want the answer in meters...

Any ideas? Am I overlooking something?

OlderDan

Homework Helper
I see no way to resolve this. Some information has been left out of the problem.

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