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1) A thin rod, length L hinged at one end, connected to a spring at the other end. Take the spring constant to be K. What is the angular frequency?

My solution:

let the displacement from equil. to be X

F=-kX

Torque= K.X.L=I a

a=K.X.L/I =L @ @ is the angul. aceleeration

@= KX/( 1/3 ML^2) = W^2X

W= (3k/ML^2)^0.5

2) Find the angular frequency of a small cylinder mass m, radius r, rolling in a cylindrical shell of radius R.

My sol.

aceleration=gsin@ let @ be the small change in angle

gsin@=R( Aceleration ,A)

A= gsin@/R

A= R angular acele. Since @is small, Sin@=@

g@/R=R angular a

angular a = w^2 @

w=(g/R^2)^0.5