- #1

Nikstykal

- 31

- 1

## 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...

mgL

_{2}- kx

_{1}= I

_{0}θ" (mass force positive since displacement is positive in the negative y direction)

x

_{1}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, x

_{1}=(L1/L2)x. Then I know x = rθ, differentiate with time twice to get x" = r θ" so then θ" = x"/r, where r = L

_{2}. Now we have ...

(I

_{0}/L

_{2})x" - k(L1/L2)x= mgL

_{2}===> (I

_{0})x" + k(L1)x = mgL

_{2}

^{2}

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.

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