Period of Oscillation of a Meter Stick

AI Thread Summary
The discussion focuses on deriving the period of oscillation (T) for a meter stick suspended at one end, questioning the formula T = 2*sqrt(2I/mgL) for small amplitudes. Participants express confusion about the absence of π in the equation, contrasting it with known formulas for simple pendulums and spring systems. Suggestions include considering small angle approximations for sine and cosine functions and applying energy conservation principles. The importance of understanding rotational inertia (I) and its relation to mass (m) and gravitational acceleration (g) is emphasized. Overall, the thread seeks clarity on the derivation process and the correct application of physical principles.
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Homework Statement



Measure the period of oscillation of a meter stick suspended at one end for small amplitudes.
Does T = 2*sqrt(2I/mgL) when I is the rotational inertia about one end? Derive this relation.


Homework Equations



I = rotational inertia
m = mass
g = gravitational acceleration
T = period of oscillation

I=mr^2

T=2*pi*sqrt(L/g)

The Attempt at a Solution



I'm not going to lie, I have no idea where to start. Previous period of oscillation problems with a simple pendulum or a spring/glider system were based off of the formula for period that included 2pi divided by the angular frequency. I don't know where the pi went or what to do with the r value if I was to substitute it in. HELP!
 
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I think your equation is missing a π in it.


Anyhow, try considering that at a small angle, what the height is (above the lowest point).

For θ being small, what is cosθ and sinθ equal to?

Now try conserving some energy.
 

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