Equations of Motion w/ spring scale

[Nikstykal]

Homework Statement

http://imgur.com/a/X7mWA

Homework Equations

1. ΣF = m a
2. Στ = Iθ"

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.

 

[malemdk]

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

 

[rude man]

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.

OK up to here.

Now we have ...
(I₀/L₂)x" - k(L1/L2)x= mgL₂ ===> (I₀)x" + k(L1)x = mgL₂²

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.