Part 4: Physical PendulumTheoretical calculationsConsider a thin uniform stick of mass M and length L. This stick is set on a pivot(black circle) a distance h from its center of mass as shown. If the stick is pulled backan angle 0 the torque on the stick due to gravity is T = -Mghsin0. The rotationalversion of Newton's 2nd Law, ET = Ia, then becomes:d²(0)-Mghsin(0) = Idt2(3)In the small angle approximation, Eg. 3 becomesdt2d² (0)Mgh 0, which againMghhas a solution 0(t) = 0ocos(wt + ø) with w =1. Noting that the parallel axis theorem gives us Iand using the equations above, show that the period can be expressed as:=ML2+ Mh?Iсм + Mh?MgL² + h²12T = 27gh2. Calculate the value for h which gives the minimum period, assuming L=1m (ourmeter stick). h

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