Oscillating rectangular plate

AI Thread Summary
To find the period of small oscillations for a rectangular plate suspended at its corner, the formula T = 2π(I/mgl)^(1/2) is used, where I is the moment of inertia and l is the length of the equivalent simple pendulum. The moment of inertia for the plate is correctly calculated as I = m/3(a^2 + b^2). The length l is determined to be the diagonal, l = (a^2 + b^2)^(1/2), which is also confirmed as correct. Some participants noted that while the calculations can become complex, simplifications may be possible by manipulating exponents. The discussion emphasizes the importance of correctly applying physics principles despite potential complications in calculations.
shizzle
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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!
 
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shizzle said:
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. :-p The moment of inertia is correct. :-p
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? :biggrin: Phyiscs is not always simple.

Daniel.
 
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
 
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