How Many Oscillations Occur Before Amplitude Decays to e^-1?

[mihir871]

[SOLVED] Oscillations Problem: Please help

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I don't even know how to start this

Thanks so much!

 

[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?

 

[mihir871]

is t= m/b?

 

[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?

 

[mihir871]

Um i got 24.2

 

[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?

 

[mihir871]

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

but i don't see where the period comes in

 

[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?

 

[mihir871]

Im completely lost now

 

[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.

 

[mihir871]

got it thanks so much!

 

[G01]

Good Job!

 

[silently_loud]

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

 

[G01]

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

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!

 

[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?