Problem Solving Strategies

7:38 AM

@JohnRennie PLease ping me when you get free

2 hours later…

9:21 AM

@Aladdin hi. Sorry to be so long replying. It's a Windows update weekend and I had lots of server problems to fix. I'm here now for a few hours.

@JohnRennie Hi

@Aladdin hi :-)

9:42 AM

Hi @JohnRennie, I have got a problem to ask, are you free?

@AjayMishra hi yes I'm free :-)

Guru Vishnu

@JohnRennie: Hi sir :-)

What I thought the answer was is $\dfrac{\omega_{+} + \omega_{-}}{\omega_{+} - \omega_{-}}$

But that is wrong.

@AjayMishra I have no idea I'm afraid. The last time I did this stuff was 40 years ago, and while I still remember the basic mechanics more advanced stuff like coupled system long ago escaped my memory. Sorry :-(

@GuruVishnu hi :-)

Where $\omega_+$ is higher normal mode frequency and $\omega_{-}$ lower normal mode frequency.

@JohnRennie No problem, thanks. :)

9:47 AM

@AjayMishra Isn't it just half the beat period?

i.e. $\omega+ - \omega-$

I didn't get you. (By the way, I think I have forgot to add the factor of 0.5 in my expected answer)

@JohnRennie What is $\omega_-$, I have merely given the ratio of upper and lower normal mode frequency.

@AjayMishra you have the two normal modes, and when you combine them you get a beat frequency equal to the difference in the frequencies of the normal modes.

The period of that beat is the time for the amplitude of the modes to change from maximum to minimum and back again, so half this period is the answer to the question.

Yeah, I've considered that. The beat frequency would be $ \dfrac{1}{2} (\omega_+ - \omega_-)$

And the underlying wave would have frequency of $\dfrac{1}{2} (\omega_+ + \omega_-)$

I didn't get you there, the period is not asked in the question.

@AjayMishra the question is effectively asking for the time taken for the amplitude of the higher frequency mode to change from a maximum to a minimum.

It asks for the number of oscillations, but that's just the time divided by the period of the normal mode.

Still, the answer is not. $\omega_+ + \omega_-$

9:56 AM

Have you been given the answer?

Oops, yes sorry, that's in the question.

Lets call the higher frequency mode 100, then the lower frequency mode will be 1.

Why?

because the spring constants differ by a factor of 100

$ \omega_- = \omega_n = \sqrt{\dfrac{k}{m}}$

10:00 AM

Oops, yes, a factor of 10 :-)

Still, that's not right.

OK, I give up. Sorry :-(

$\omega_+ = \sqrt{w_n^2 + 2w_s^2}$

Where $\omega_n = \sqrt{\dfrac{k}{m}}, \omega_s = \sqrt{\dfrac{k'}{m}}$

@JohnRennie Okay, thanks though.

10:40 AM

@JohnRennie Hello

@pi-π hi :-)

@JohnRennie If we have to design a program that displays the curve of functions that we have entered using C language, how can we do that?

I mean what tools do we need for this?

I'm busy for a few minutes. I should be free soon.

@JohnRennie Okay. Please ping me when you are free.

11:23 AM

@JohnRennie Hi

@pi-π hi. I'm free for a few minutes. What did you want to ask?

@JohnRennie If we have to design a program that displays the curve of functions that we have entered using C language, how can we do that?
I mean what tools do we need for this?

Do you mean the user types a function and your program has to display it as a graph?

@JohnRennie Yes. Display the graph

What sort of things can the user type? Is there a limited list of functions? Presumably there must be some limitations as there is a potentially infinite number of functions the user could type.

@pi-π hello?

11:30 AM

@JohnRennie The functions are limited. We are only considering Inverse Circular Functions, Algebraic, Logarithmic, Trigonometric and exponential

And simple transformations like replacing x by x+a or x-a or by kx or by k/x ...

So I guess the input would be a function name, e.g. sin or exp, and a minimum and maximum value of x. Then your function would graph y(x) over the requested range.

@JohnRennie Yes. Something like that only

That all seems straightforward. The only difficult bit would be figuring out how to produce the graph. You need some form of graphics package.

Are you using GNU C? Or Microsoft C? Or some other compiler?

@JohnRennie gcc compiler

To be honest I don't know what graphics packages are good to use with GNU C.

11:39 AM

@JohnRennie Okay

plotutils?

Plotutils

GNU plotutils is a set of free software command-line tools and software libraries for generating 2D plot graphics based on data sets. It is used in projects such as PSPP and UMLgraph, and in many areas of academic research, and is included in many Linux distributions such as Debian and cygwin. Windows and Mac OS X versions are also available. The library provides bindings for the C and C++ languages. Its stand-alone command-line tools can generate graphs and perform numerical calculation of spline curves and systems of ordinary differential equations. Plotutils is a GNU package and is ...

If this is for college work you might find they recommend a plotting package.

@JohnRennie will u be back later

@JohnRennie They should have recommended but they didn't.

@Aladdin I'm here for another hour, then I won't be back until tomorrow. Do you want to chat now? I don't think there is much more I can say about GCC plotting packeges.

Yes

Ajay Mohan

11:42 AM

I have a question, John. I'll ask after Aladdin's finished with his topic.

@AjayMohan post the question now, and I'll look at it as soon as I can.

Ajay Mohan

Alright. Consider the problem of a general surface charge distribution $\sigma(\theta,\phi)$ on a sphere of radius $R$. I want to show that $\lim_{r \to R^+} \partial_r \Phi(r,\theta,\phi) - \lim_{r \to R^-} \partial_r \Phi(r,\theta,\phi) = - \frac{\sigma(\theta,\phi)}{\epsilon_0}$. This can be shown using an infinitesimal gaussian cylindrical surface covering the area of interest. But, I'm asked to show it using the Green's function solution for $\Phi$ (equation $(2)$ in the above picture).