1. Nov 21, 2007

### mihir871

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

A 290 g air-track glider is attached to a spring with spring constant 4.10 N/m . The damping constant due to air resistance is 2.40×10^−2 kg/s. The glider is pulled out 28.0 cm from equilibrium and released.

How many oscillations will it make during the time in which the amplitude decays to e^-1 of its initial value?

2. Relevant equations

$$\omega=$$2$$\pi$$/T
T=2$$\pi$$$$\sqrt{m/k}$$
Damping: x(t) = Ae$$^{-bt/2m}$$cos($$\omega$$t)

3. The attempt at a solution

I dont even know how to start this

Thanks so much!!

2. Nov 21, 2007

### G01

Well, we know the damping coefficient, b, correct? Can you use this to find the time it takes for the oscillation to decay the specified amount?

Last edited: Nov 21, 2007
3. Nov 21, 2007

### mihir871

is t= m/b?

4. Nov 21, 2007

### G01

Your a little off. Consider this:

The amplitude of the wave at any time t is given by:

$$Ae^{-bt/2m}$$

The initial value is A, so we want to know the time that:

$$Ae^{-bt/2m}=Ae^{-1}$$

What does this equation give you for the time?

5. Nov 21, 2007

### mihir871

Um i got 24.2

6. Nov 21, 2007

### G01

Sounds good to me. Now can you take this time value and use it to find out how many oscillations the system undergoes in that time? HINT: You'll need the period. How can you find that from the known information?

7. Nov 21, 2007

### mihir871

from Period= 2pi(m/k)^.5

but i dont see where the period comes in

8. Nov 21, 2007

### G01

Oops! I meant to say the frequency, sorry! The frequency gives you the number of oscillations in one second, correct? So, using that, how many oscillations in 24.2 seconds?

9. Nov 21, 2007

### mihir871

Im completely lost now

10. Nov 21, 2007

### G01

You want to know how many oscillations happen in 24.2 seconds, correct?

Well,

the # of oscillations in one second = frequency

So if you know the frequency, you know the number of oscillations in one second. Using that information, it is a basic math problem to find the number of oscillations in 24.2 seconds. You know how to do this part if your this far into a physics course. Think about it.

11. Nov 21, 2007

### mihir871

got it thanks so much!!!

12. Nov 21, 2007

### G01

Good Job!

13. Nov 21, 2007

### silently_loud

Wow, someday I will be able to do that lol. GO1 recommend any sources for physics tutorials or something?

14. Nov 22, 2007

### G01

The one that is always recommended around here is hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

This is a good tutorial and it is trustworthy and accurate.

If this doesn't satisfy your curiosity then I would suggest investing in a textbook. Good luck!

15. Nov 22, 2007

### silently_loud

Thanks. Really interesting stuff, really like the website. What text would you recommend for a beginner, I am taking physics now but its easy. Lately we have studied frictional forces such as F=un and F=ma, but this is over my head. Go1 what degree do you have?