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. :tongue2: The moment of inertia is correct. :tongue2:
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. :yuck:

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