An attempt frequency for a harmonic oscillator?

[Duave]

An "attempt frequency" for a harmonic oscillator?

Homework Statement

What is the "attempt frequency" for a harmonic oscillator with bound potential as the particle goes from x = -c to x = +c? What is the rate of its movement from -c to +c?

Homework Equations

v =$\frac{1}{2π}$$\sqrt{\frac{k}{m}}$

ω=$\sqrt{\frac{k}{m}}$

The Attempt at a Solution

1. x(t) = Acos(ωt)

2. $\frac{d x(t)}{dt}$ = -Aωsin(ωt)

3. v(t) = $\frac{d x(t)}{dt}$

4. v(t) = -Aωsin(ωt)

5. -$\frac{v(t)}{Asin(ωt)}$ = ω

6. ω = -$\frac{v(t)}{Asin(ωt)}$


4. Conclusion


Is the expression (equation) below the proper equation to use to determine the "attempt frequency" for a harmonic oscillator with bound potential as the particle makes its way between x = -c and x = +c?

ω = -$\frac{v(t)}{Asin(ωt)}$?

 

[Simon Bridge]

Define "attempt frequency"?
Define "rate of movement"?
State these definitions in words and compare with what you've done.

 

[Duave]

Thank you very much Simon.

The only problem is I've looked all around the universe and could barely even find a source that said even literally said "attempt frequency". I don't know what the definition is.

And, "rate of movement" to me is defined by some measurement over time, but, I still can't put 2 and 2 together, just because it's definition is so straight forward.

I wrote all the things in my question, because I needed someone to correct it for me. I'm have not found anything that could confirm its "correctness".

Thanks

 

[Simon Bridge]

If you don't know what those two terms mean, then you cannot do the problem.

Googling "attempt frequency" gets lots of examples of it's use.

Googling the "definition attempt frequency" suggests:
"attempt frequency" is the rate that a bound particle "attempts" to escape the potential.
http://encyclopedia2.thefreedictionary.com/attempt+frequency
... so how many opportunities per second does the particle have to escape?

"rate of movement" could refer to dx/dt - the velocity ... but why not just say "velocity"?
It could also refer to the rate that particles escape the well.

Both of these are used quite a lot.

What does the value of c signify? Is it the classical limits for a particle with a particular energy or some arbitrary point inside those limits?

If this is part of coursework then you should have had these terms used as part of the course somewhere.
The context will help - like: is this part of the course on SHM in general or about nuclear physics or what?
Since you have not found any such reference - you should go ask the person who set the problem.

 

[Duave]

Simon,

-c and +c are the bounds. Okay look at this:


1. x(t) = Acos(ωt)

2. $\frac{d x(t)}{dt}$ = -Asin(ωt)

3. $\frac{d x(t)}{dt}$ = v(t)

4. $\frac{d x(t)}{dt}$ = velocity

5. v(t) = -Asin(ωt)


How does step five look? I even took the derivative of the position, which would be the velocity.

Thanks again

 

[Simon Bridge]

You have decided to interpret "rate of movement" to mean "velocity"?
Step 2 is incorrect. Hint: chain rule.

You could have checked this yourself by checking that the units on the RHS of equ5 match the units on the LHS.