# Equations of Motion w/ spring scale

1. Feb 1, 2017

### Nikstykal

1. The problem statement, all variables and given/known data
http://imgur.com/a/X7mWA

2. Relevant equations
1. ΣF = m a
2. Στ = Iθ"

3. The attempt at a solution
First , assuming small motion, all movement of the scale can disregard x components (so the spring stretches only in vertical direction without an impact from the x directional movement). I summed torque around the pin, point O, which would be equal to the mass moment of inertia * theta double dot. so...

mgL2 - kx1 = I0θ" (mass force positive since displacement is positive in the negative y direction)

x1 is the spring movement upwards, however we want to relate that to the x displacement downwards with the mass, which we'll just call x. Now, using like triangles, x1=(L1/L2)x. Then I know x = rθ, differentiate with time twice to get x" = r θ" so then θ" = x"/r, where r = L2. Now we have ...

(I0/L2)x" - k(L1/L2)x= mgL2 ===> (I0)x" + k(L1)x = mgL22

This answer just doesn't feel right. I feel like I may not have correctly applied newtons 2nd law or maybe didn't correctly set up the kinematics. Any input would be helpful, thanks.

Last edited: Feb 2, 2017
2. Feb 2, 2017

### malemdk

You need not take into account the mass moment of Inertia of mass m, since it is a statics problem

3. Feb 2, 2017

### rude man

OK up to here.
Check your math, this has at least 2 mistakes in it. One is a sign error.
Also, what is I0? You need to express this in terms yuu were given.

Also BTW not only is this not a static question but, contary to the problem statement iself, the scale swings forever back & forth since no damping mechanism was introduced.

Last edited: Feb 2, 2017