1. ## Particular Inegral

$m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$

I am trying to find the general solution.

Setting
$\omega^2=\frac{k}{m}$, I found $x_c$ to be:

$x(t) = A~cos \left ( \sqrt 5 \omega t + \phi \right )
$

I have no idea how to find $x_p$...

What trial solution would you suggest using?

2. Hello,

You can consider that x is a constant. Thus its second derivate will be null and you'll have an equation with xp

I hope for you it's true that $\omega^2=\frac{5k}{m}$, because this is something i can't do ^^

3. I am totally new at this... I still have no idea.

I divided the original equation through by $m$ to get:

$\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0$

am i getting any closer?

4. I really don't know for xc... I don't remember the rules for general solution ! If you're not sure, derivate again to see if you get xc so that xc is solution of d²xc/dt²+5w²xc=0

However, for xp :

xp is a particular solution. Let X be a constant satisfying the equation.

The second derivate of X is 0.

We have $5kX = -mgsin\alpha + 11kl_0$

-> $X=x_p=\frac{-mgsin\alpha + 11kl_0}{k}$

5. I don't get it. Where did the 5 go?

I did this:

$
m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$

$
\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0
$

$
\frac{d^2x}{dt^2} + 5\omega^2 x = \omega^2 (11l_0-\frac{mg}{k}sin\alpha)
$

$
x_p=\frac{1}{5}(11l_0-\frac{mg}{k}sin\alpha)
$

How's that? Anyone? Anyone?

6. Am sorry, i forgot the 5...

7. So we pretty much have the same answer. Thanks for the help!

8. Originally Posted by billym
I don't get it. Where did the 5 go?

I did this:

$
m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$

$
\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0
$

$
\frac{d^2x}{dt^2} + 5\omega^2 x = \omega^2 (11l_0-\frac{mg}{k}sin\alpha)
$

$
x_p=\frac{1}{5}(11l_0-\frac{mg}{k}sin\alpha)
$

How's that? Anyone? Anyone?
Relax guy. Be vague.

Moo dropped a 5. It was a simple error, easily spotted. As you did. If you understand what Moo was doing to get the particular solution, then all's well. So go back, put the 5 in where it's meant to go. There's the answer.

Life's full of small mistakes, most easily spotted and corrected for. The world keeps turning. Don't have cow, man.

9. Don't have cow, man.
Moo
Thanks for explaining it more precisely than i did ^^

10. I really wasn't having a cow man! I seriously wasn't sure if she dropped the 5 on purpose or not. This site feels like I'm doing my homework with God, so I just assume everyone else is right.

11. Originally Posted by billym
I really wasn't having a cow man! I seriously wasn't sure if she dropped the 5 on purpose or not. This site feels like I'm doing my homework with God, so I just assume everyone else is right.
Not at all, we're all equal in front of maths

errare humanum est

Btw, what does "have a cow" means ? ^^'

12. He was likening my concern over your missing 5 to the ordeal of giving birth to a cow.