>>7982742
Look up Fourier transforms, transfer functions and how they are used to solve differential equations

>>7982758

I do not think that is relevant desu

>>7982742
What book is that? because its written like shit

What he does is let [math] x(t) = \hat{x}e^{i\omega t}[/math] with [math] \hat{x} [/math] some constant because you know that the position will be a function of [math] t [/math] only in that form.

Plug this into equation 23.3 and differentiate and you get 23.4

>>7982932

How does he know that the angle of the complex number is wt?

oh and the book is vol 1 of the Feynman Lectures.

>>7982994
>>7982994
You should probably study complex numbers before doing any of this, but it's because if you consider any point the in complex plane, say z= a+ib, if you want to geometrically find the distance from the origin to that point, you find that the distance is a^2+b^2 (=R), ie: the modulus of the complex number.

If you want to geometrically find the angle (t) that the line from the origin to the point makes with the real axis, you first find that a=Rcos(t) and b=Rsin(t). Then you can write again z=a+ib = R( cos(t) + isin(t) ). But the magical Oiler formula says e^(it) = cos(t) + isin(t). So the complex number now becomes z=Re^(it). So the angle of any complex number Re^(it) [btw all complex numbers have this form] is t and its magnitude is R.

>>7982994
Its an assumption that you show works in the end.

You can pick another frequency [math] \omega_1 [/math] if you arnt convinced that they must be the same.

You then end up with
[eqn] \left(i\omega_1\right)^2\hat{x}e^{i\omega_1 t} + \frac{k}{m}\hat{x}e^{i\omega_1 t} = \frac{F}{m}e^{i\omega t} [/eqn]

Factoring out the exponential then gives you

[eqn] \left(i\omega_1\right)^2\hat{x} + \frac{k}{m}\hat{x} = \frac{F}{m}e^{i(\omega-\omega_1) t} [/eqn]

Bu the left side, and F/m is independent of [math] t[/math],so [math] e^{i(\omega-\omega_1) t}[/math] must be independent of [math] t[/math], which is only true if [math] \omega - \omega_1 = 0[/math].

Basic he knows the answer and uses an assumption that works. This method is used a lot to solve equations. if you have a function [math] f(x,t) [/math] in a differential equation, try and write it as [math] f(x,t) = g(x)f(t) [/math] and see if you get a not trivial answer. IF you do then the assumption was correct, if you don't, then it was wrong and you try something else.

>>7983027

Yes, I am familiar with that. I was just confused as to how he magically knew that the angle was related to omega.

>>7983031

Oh. Thats kind of disappointing in a way. It feels like cheating to solve something with the assumption that you already know the answer.

I think I get it now though, thank you.

>>7982932
>the book is vol 1 of the Feynman Lectures.
Damn, so it was Feynman?
Somehow, I could tell from the way it's written.

>>7982994
Only Feynman Lectures 2 is good.

>>7983046

I assume I have to finish 1 in order to "get" 2 though, right?

>>7983050
I dont know, ive never read it.

>>7982932

tbf its not so much that the book sucks, just that when the book was written 30-odd years ago maths was taught in a very different way

>>7983055
it's clear that it's not a math book
it reads like a book for engineers / people who don't do math and confirmed, it's the Feynman lectures.

many 30 years old math books are amazing

>>7983055
>30-odd years ago maths was taught in a very different way
Be that as it may, it's not the reason the book is usually not recommended to someone learning the material the first time.
Feynman basically admits that the book/lectures the book is based on did not really help his freshmen students to solve problems. I only have volume 2 here which basically confirms this, but I think it's in volume 1's preface.
These books are hard to penetrate because a) Feynman is a genius who sought many different ways to describe the same problem, and I guess not always did the most intuitive ones make it into the book, and b) he uses his vast intuition and set of tricks gained from experience, neither of which a first time learner usually has.

Of course you are lost, complex numbers doesn't represent any real world situation.

Learn differential equations. First solve the homogenous equation LHS=0 by trying x_h=exp(rt) where r is a constant. Then use variation of parameters to find a particular solution.

>>7983096

Im liking it so far.

I can see that if this information was in lecture form people would struggle, but since im able to go back and reread unclear bits repeatedly I find it very helpful.

Plus I adore the example proofs and derivations

>>7983055
You mean without all the technobabble and unnecessary obfuscation of information and abstraction--as if the text was basically written in a foreign language--that plagues today's publications?

I, for one, like calling a cat a cat, instead of a habitually prone pelaged quadriped of the Felidae family.

Also, you don't just turn information into some kind of literary interpretation competition by doing this, you also harm the education of future students. It is much easier for a student to read about some guy who discovered phenomenon x by having that guy (or some other guy) describe the thought process behind his thinking, e.g. "I considered two marbles rolling in parallel down a slope" (which is his real thoughts) instead of "I considered an n-matrix of two orthogonally unilaterally oscillating n-spheres" (which is the abstraction made after the fact).

Keep in mind that I am not arguing against the use of specialized terminology, I am arguing against the use of specialized terminology when it is clearly unnecessary, and this happens a lot in modern publications. Also, if you only teach the resulting abstractions of the original thoughts, it is obviously much harder to intuit the concept.

>>7983136
Yes, one of the complaints of students who struggled with the lectures Feynman gave was that there was no accompanying book, because the style Feynman taught was unconventional.
The books on the lectures would remedy this, and there is also "Tackling physics problems", an accompanying book that helps with the other flaw I mentioned.

But I am sure one can greatly benefit from the books whether one knows the material or not.

>>7983149
I don't see why it's unnecessary. If the researcher was able to view a cat as a habitually prone pelaged quadriped of the Felidae family in a way that allowed him to think more clearly about the problem being solved, I think this is a positive. Sometimes when something is cast in a completely different setting, you're able to see something that wasn't apparent before, e.g. using complex exponentials to represent oscillations as Feynman does. Nobody is complicating things to make it more difficult; rather, this is simply the way they think about it.

>>7982932
>not recognising Feynman lectures
>being a fag

>>7983050
No, you can pretty much pick and mix between them. Vol.2 has a small intro to vector calculus - enough you need to do simple electrostatics problems

>>7983096
The book is lovely to read as someone who has gone through the material before with different books. The insights and connections he makes are beautiful and worthwhile.

>>7983208
Indeed, that is where the books really shine.

>>7983198
I tried reading them after studying physics, didnt get very far, then skipped ahead and tried some more, still couldn't get very far. then dropped it and read better books. I find his writing style really annoying.