## anonymous one year ago Setting up a differential equation? Attachment below~

1. anonymous

I am sure I have.. or am going the wrong direction. How do I create a differential equation from the following data?

2. IrishBoy123

without knowing the details, you're missing an R on the friction term and the signs are wrong [though they do correct themselves in the second line....] :p

3. anonymous

I am trying to do this from formulas, and have trouble finding ... the relevant formulas :x

4. anonymous

I managed to do this without any fraction (no dampening) using the ...Force moment formula $-mglsin(\phi) = I_0\frac{ d^2\phi }{ dt^2 }$ where I is $I_0 = mR^2$

5. anonymous

However, I am not sure how to... apply this with a friction :s

6. anonymous

Appreciate your help - Physics section is very inactive compared to the math section :)

7. IrishBoy123

think you might wish to explain the physical situation/context eg post/link the original question in meanwhile, and guessing the situation, around the centre of rotation $$mR^2 \, \ddot \theta = - mg \sin \theta \, \cdot R+ \mu mg \cos \theta \, \cdot R$$ at this point, normally, you would linearise, $$\lim\limits_{\theta \to 0} \sin \theta \approx \theta$$ $$\lim\limits_{\theta \to 0} \cos \theta \approx 1$$ that would leave you with $$\, \ddot \theta + {g \over R} \theta = {g \over R} \mu$$

8. anonymous

Hmm... I don't understand why there is an R - I mean, if you decom.. dec... move it around I dont get an R - do the R has something to do because its going in a circular motion?

9. anonymous

If we only look at one of them - for example the µmg*cos(phi)*R. How do we... get to that? Especially with the R @IrishBoy123

10. IrishBoy123

it would great make sense to post the actual physical question, if you have one. you say friction plays a role here, but as this looks like a simple pendulum problem [$$\ddot \theta = - k \theta$$], i have responded on the basis there is some physical aspect that means you can just add in a frictional force ......which you can, without it having any real physical meaning...... but it would still make a lot more sense to be talking about a concrete example.

11. anonymous

If I translate the text (roughly); ------ A point shaped pendel sliding on a surface. The surface is on pair with a circle and has radius 1m. Draw a figure, write all the relevant forces and formulas and calculate your way to a differential equation

12. anonymous

Appreciate the help - Going to work more on this