Physics Question?

Question

Two identical thin rods, each of mass m and length L, are joined at right angles to form an L-shaped object. This object is balanced on top of a sharp edge. If the object is displaced slightly, it oscillates. Assume that the magnitude of the acceleration due to gravity is g .

1) Find w, the frequency of oscillation of the object.
Your answer for the frequency may contain the given variables m and L as well as g.

Answer 1

You have a pendulum that oscillates an 'imaginary " bob of mass m and attached to the string of length l located below the sharp edge.

w=sqrt(l /g)

Lets find l
l - y-centroid = yc

yc = (sum of moments)/ (sum of masses)

M1=M2= y m
y - arm of rotation of the center of the rod's mass about x - axis.

y= L/(2 sqrt (2) )
M1+M2= 2 [L/(2 sqrt (2) )]m= [L/ sqrt (2) ]m
l= m[L/ sqrt (2)] /2 m
l=L/(2 sqrt (2) )

now
w= sqrt([L/(2 sqrt (2) )]/g)
f=(1/(2 pi)(sqrt([L/(2 sqrt (2) )]/g))