# Homework Help: Spring mass system attached to a disc

1. May 9, 2017

### rafaamcarvalho

Hello to all, first sorry about any mistakes because English is not my native language. I'm trying to solve this problem and I can't seem to find the equation of motion
1. The problem statement, all variables and given/known data

The disc and the point A both have mass m;
θ(0) = 0

2. The attempt at a solution
I tried to use the newton's second law for rotation but I can't find the values of the point A and K in therms of θ.
I don't know if what I did here was correct, but I tried this:

ΣMo = Jα
Jα = m⋅g⋅r - k⋅x⋅r; x = r⋅sinθ

2. May 9, 2017

### haruspex

Is this for small oscillations only, or can θ be anything? If anything, the mgr term is wrong.
It looks to me that the strong wraps around the disc, so it is not sine θ. If the disc has rotated θ, what length of string is wrapped onto it?

3. May 9, 2017

### rafaamcarvalho

I believe so. But if its not m⋅g⋅r, what could it be?

You are right, the spring wraps around the disc, so is the displacement x = r⋅θ?

And how to calcule the polar moment of inertia J of a disc with mass m with a concentrated mass m in point A?

4. May 9, 2017

### haruspex

Draw the diagram showing the line of action of mg. For the moment of a force about an axis, you multiply it by the perpendicular distance from its line of action to the axis.
Find the moment of inertia of each mass around the axis and add them.

5. May 9, 2017

### rafaamcarvalho

Oh got it, did not check if it was perpendicular, so the therm should be m⋅g⋅cosθ⋅r?

And then my final formula would be,

(m⋅r² + ½⋅m⋅r²)α + (k⋅r²)⋅θ - (m⋅g⋅cosθ⋅r) = 0 ?

6. May 9, 2017

Looks right.