# Homework Help: Oscillation problem

1. Jun 17, 2009

### Noiro

1. The problem statement, all variables and given/known data

Steel ruler tip's oscillation amplitude is 1cm, frequency 5Hz. What is the path the ruler's tip goes within 2 seconds?

2. Relevant equations

I think I need to find a period so the equations would be T=1/5 s but I'm not sure.

3. The attempt at a solution

I don't know how to solve it so I would be grateful if someone could help me.

2. Jun 17, 2009

### Hootenanny

Staff Emeritus
What does the question mean by "path"? Does it mean the arc length, or the normal deviation, or the tangential deviation?

3. Jun 17, 2009

### Noiro

It is the arc length

4. Jun 17, 2009

### Hootenanny

Staff Emeritus
Oke doke.

As you correctly say, the period of oscillations is 1/5 seconds. What else do you think we need to work out in order to solve this problem?

5. Jun 17, 2009

### Noiro

Maybe a phase of an oscillation? I'm not sure though. What do we need?

6. Jun 17, 2009

### Hootenanny

Staff Emeritus
What do you usually need to work out the arc length (two things)?

7. Jun 17, 2009

### Noiro

Measure of a central angle and radius?

8. Jun 17, 2009

### RoyalCat

Scratch what I said for now.
Not to interlope, but the arc length is given, and you can't calculate it using the central angle and radius as those are unknowns for this problem.

I think what Hootenanny was trying to steer you towards was the distance traveled per period, try finding that and then try and see what distance the tip travels in 2 seconds.

Last edited: Jun 17, 2009
9. Jun 17, 2009

### Hootenanny

Staff Emeritus
Correct. So, what is the radius?

10. Jun 17, 2009

### Hootenanny

Staff Emeritus
No it isn't, the amplitude is given, but that isn't the arc length.
Erm... yes you can.

Last edited: Jun 17, 2009
11. Jun 17, 2009

### Noiro

I don't know. What is it?

12. Jun 17, 2009

### Hootenanny

Staff Emeritus
You have to work it out...

HINT: If you weren't given the frequency, but were instead given the radius of the pendulum, what equation would you use to determine the period of the oscillations?

13. Jun 17, 2009

### Noiro

I think it's T=2pi sqrt(L/g)

14. Jun 17, 2009

### Hootenanny

Staff Emeritus
That is correct.

Just one minor point, do you have a diagram associated with this question? I'm assuming that this steel rule is hanging vertically and is oscillating in plane like a pendulum. Would that be correct?

15. Jun 17, 2009

### Noiro

No it's embedded in a clamp. I hope you can imagine what it looks like.

16. Jun 17, 2009

### ideasrule

C'mon, get on MS Paint and draw a diagram. A lot of us here are lazy. :shy:

17. Jun 17, 2009

### Hootenanny

Staff Emeritus
Ahh I see. I had originally envisaged a pendulum-like set up. However, this case actually turns out to be a lot simpler than the case that I had originally envisaged. The steel rule is acting like a mass-spring system and in this case to a fairly high degree of accuracy the tip of the rule doesn't trace an arc. Instead, it traces [approximately] a straight line.

So, let's forget about determining the radius. Instead, can you tell me how far the tip of the rule travels in one complete oscillation?

18. Jun 17, 2009

### Noiro

Well if amplitude is 1cm then I guess it's 2cm. Am I right?

19. Jun 17, 2009

### RoyalCat

Amplitude is the maximal displacement from the point of equilibrium.
The period is the length of time it takes the particle to return to its initial position, the length of how many amplitudes would a particle have to cover in distance over the course of 1 period?

Another hint:
This little diagram should hopefully make the point a bit more clear:
|---eq---|
--- is the amplitude, not --- ---.

20. Jun 17, 2009

### Hootenanny

Staff Emeritus
As RoyalCat has said, 1cm is the maximal displacement (i.e. the distance between its equilibrium position and one of the turning points). What is a full oscillation in terms of turning points and the equilibrium position?

21. Jun 17, 2009

### Noiro

So it's 4cm right?

22. Jun 17, 2009

### Hootenanny

Staff Emeritus
Correct. So, if the ruler has a period of 1/5 seconds, how many oscillations occur in 2 seconds? Hence how far does the tip of the ruler travel in 2 seconds?

23. Jun 17, 2009

### Noiro

So in 2 seconds occur 10 oscillations and tip of the ruler travels 40cm. Am I right?

24. Jun 17, 2009

### Hootenanny

Staff Emeritus
Sounds good to me!

Apologies for the earlier confusion regarding the orientation of the ruler. Thanks to RoyalCat for pointing out the correct set up.

25. Jun 17, 2009

### Noiro

No problem. Thanks Hootenanny and RoyalCat you really helped me!