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

[kkred]

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

 

[trust143_raj]

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.

 

[kerimek]

. To find the angular frequency, we can use the formula for simple harmonic motion: ω = √(k/I), where ω is the angular frequency, k is the spring constant, and I is the moment of inertia. In this problem, the moment of inertia can be calculated using the given information as I = (1/3)*M*L^2 = (1/3)*2kg*(1m)^2 = 2/3 kgm^2. Plugging in the values, we get ω = √(1000 N/m / 2/3 kgm^2) = √(1500 s^-2) = 39s^-1. This is the angular frequency of small oscillations of the plank.