Recent content by Holali

"" udu=f(y)dy The left side is, of course, (1/2)u2, the reason for the name "quadrature". we have (1/2)u2=∫f(x)dx "" DIdn't you change y for x in this part?

Hi, simple question, but difficult to find an answer for me How to integrate sqrt((ax+b)/x) dx ? a,b constants and x variable if it matters, I would be happy if you could solve it just for both a,b >0 Thanks

Hmm, chain rule.I found it at wikipedia,but can't understand it. I understand equation y''=dy'/dx, but not y''=y' dy'/dy. Could you show me some easy example, like y''=2y^2, or y''=y^2 -y ?

Hi, simple quetion, as you can see in the title. How can I solve differential equation y(x)''=f(y(x)) I know I can write first derivative like dy/dx. But how can I write second derivative in such form? If it would be y(x)'=y, then it can be written dy/dx=y => (1/y)dy=(1)dx => I can...

Well, it can be also thin rod. I originaly meant a long prism with square base. But rod is fine too. Does it matter a lot if it has square or circular base? (if the volume and mass are the same). We can use anything long with known moment of inertia. And yes, the force is all the time acting...

Ok, thanks for all posts, its become quite big discussion here. Can someone make some conclusion now? The best way to understand this problem is via an example. If the plank has the mass m=2kg and length 12m, the force pushing it is in distance d=3 meters from the centre of the mass and F=4N...

Thanks for your replies, but there are still unsolved things: How fast will the plank rotate and around what point? (are you sure it will be around centre of the mass?) And what will be the speed of translational motion?

Hi, I would be happy if you could solve and explain following problem: Imagine some solid long object (wooden plank for example) being just like that in vacuum, free, without being fixed to any point of space. Then, imagine only one forse pushing this object in a certain point of object...

Hi, I would like to calculate one integral. I just want to get primitive function, not definite integral. ∫ 1/(x^2+a) dx where a is real number and >0 I only found that ∫ 1/(x^2+1) dx , its arctan(x) + C, but i don't know how it is with different 'a' values. Thanks for help!