Oscillating rectangular plate

[shizzle]

How do i find the period of small oscillations and length of the equivalent simple pendulum, for a rectangular plate (edges a and b) suspended at its corner and oscillating in vertical plane?

T = 2pi (I/mgl)^1/2
i calculated l (length) to be (a^2 + b^2 )^1/2 ---(the diagonal) is this right?

I = m/3 (a^2 + b^2)

when i try to plug this into T though, it gets nasty and I'm not sure this is right. help!

 

[dextercioby]

How do i find the period of small oscillations and length of the equivalent simple pendulum, for a rectangular plate (edges a and b) suspended at its corner and oscillating in vertical plane?
T = 2pi (I/mgl)^1/2
i calculated l (length) to be (a^2 + b^2 )^1/2 ---(the diagonal) is this right?
I = m/3 (a^2 + b^2)
when i try to plug this into T though, it gets nasty and I'm not sure this is right. help!

1.I guess last night's discussion really helped. The moment of inertia is correct.
2.The initial formula is correct.
3.The diagonal is correctly calculated and it is a vertical axis for equilibrium.
4.What if it gets nasty? Phyiscs is not always simple.

Daniel.

 

[shizzle]

ha ha ha. I think it is possible to simplify it further actually. so...
can i simplify (a^2 +b^2) / (a^2 + b^2)^1/2 = (a^2 + b^2 )^1/2 ? simply playing with the exponents. ie. 1-1/2