A homogeneous board of length 1 and mass M stands on a hemisphere of radius R (R> 1/2) in the equilibrium position as shown in the figure. a) Find the period equilibrium position (3 points) b) During oscillatory motion, the maximum thickness of the deflection of the rod from the equilibrium position is equal to a nal- Let the amplitude of the contact force from the hemisphere to the rod at each end be equal to N. The difference N at the equilibrium position and at position a, max Can be written as AN- kMganeх- Find k (4 points) small fluctuations of boards