Aslender, uniform metal rod of mass m and length lis pivoted without friction about an axis through its midpoint andperpendicular to the rod. a horizontal spring, assumed massless andwith force constant k, is attached to the lower end of the rod, with the other end of thespring attached to a rigid support.
find the torque tau due to the spring. assume that theta is small enough that the spring remains effectivelyhorizontal and you can approximate \sin{(\theta)}\approx \theta (and \cos(\theta)\approx 1 ).
express the torque as a function oftheta and other parameters of the problem.
what is the angular frequency omega of oscillations of the rod?
express the angular frequency interms of parameters given in the introduction.