# Angular frequency of plank attached to spring

1. Feb 25, 2016

### vetgirl1990

1. The problem statement, all variables and given/known data
A horizontal plank (mass 2kg, length 1m) is pivoted at one end. A spring (k=1000N/m) is attached at the other end. Find the angular frequency for small oscillations.

2. Relevant equations
ω = √(mgd + kΔxd/I)
I think I would be treating the plank as a long thin rod with rotational axis through the end (since I'm not provided with the dimensions of the plank), so I = 1/3mL2 + md2
Where L: length of the rod, d: distance between pivot and rod's centre of mass (d=L/2)

3. The attempt at a solution
I = 1/3mL2 + md2 = 1/3mL2 + m(L/2)2

ω = √(mgd + kΔxd/I)
mgd component --> mg(L/2)
kΔxd component --> mg(L/2)2

Substituting all the known values...
ω = √[(2)(9.8)(1/2) + 1000(12)] / [(1/3)(2)(12) + 2(1/2)2]
ω = √1009.8/1.16 = 29.4

Still not getting the correct answer.

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2. Feb 25, 2016

Not so.