Question

Setting up a differential equation?
Attachment below~

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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 \[I_0 = mR^2\]

Answer 5

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

Answer 6

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

Answer 7

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 \( \, \ddot \theta + {g \over R} \theta = {g \over R} \mu \)

Answer 8

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?

Answer 9

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

Answer 10

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.

Answer 11

If I translate the text (roughly);
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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

Answer 12

Appreciate the help - Going to work more on this