Question

IV. Torsional Oscillator length I to a thin s twisted away from equilibrium it exerts a restoring torque ulum is constructed by attaching rigid rod of mass m and n vertical fiber of effective spring constant K. When the fiber on the rod which attempt oscillations, similar to the effect of spring. Assuming the re τ is relationship s to return the rod the its equilibrium position through small storing torque proportional to the angular displacement e, we can assume the empirical Fine Thread

Answer 1

We know tow = -k theta considering simple Harmonic motion if the equilibrium static of the system is disturbed then the man expression a restoring force given by Hook's law: f = -k x where k is force constant of spring according Newton's second law of motion m x = -k x this differential equation is known as SHM and the solution is x = a cos (wt - r) equating both the equation we get , -m w^2 a cos (w t - pie 0 = -k a cos (w t - pie) (1) resembling above with our given system we have tow = -k theta Therefore the rotational equation of motion of the system is I theta = tow I theta = -k theta theta = a cos (w t - pie 0 Hence the motion is S H M 14) To satisfy equation 1) only solution provided i lambda w = squareroot k/m