How Is Angular Frequency Calculated for a Plank Supported by a Spring?

AI Thread Summary
The discussion focuses on calculating the angular frequency of a uniform plank supported by a spring. Given a mass of 2.0 kg and a length of 1.0 m, the moment of inertia is calculated using the formula 1/3*M(L^2). The angular frequency of small oscillations is determined to be 39 s^-1 using the formula T=(2π(I/mgr)^(1/2)), where r is the distance from the center of mass. The process involves finding the period T and then inverting it to obtain the frequency f. This method effectively combines principles of rotational dynamics and harmonic motion.
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A uniform plank of mass 2.0kg and length 1.0m is pivoted at one end
in a horizontal plane. It is supported at the other end by a spring with
k = 1000 N/m . What is the angular frequency of small oscillations? It m
may interest you to know that the moment of inertia of a uniform rod about its end is 1/3*M(L^2) where M is the mass and L is the length.


Tried to find Angular frequency by using angular momentum but I didn't find a suitable way to do it. Any suggestions?

The answer is 39s^-1
 
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use T=(2*3.14(I/mgr)^(1/2))
r is the distance from center of mass
Then inverse T to calculate the value of f.
 

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