A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k. The moment of inertia of the plank about the pivot is . The plank is displaced by a small angle from its horizontal equilibrium position and released. (a) Show that it moves with simple harmonic motion with an angular frequency = 3k/m . (b) Evaluate the frequency if the mass is 5.00 kg and the spring has a force constant of 100 N/m.