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 (Fig P15.61). The moment of inertia of the plank about the pivot is 1/3 mL2. The plank is displaced by a small angle θ from its horizontal equilibrium position and released.
(a) Show that it moves with simple harmonic motion with an angular frequency w = √3k/ m.
(b) Evaluate the frequency if the mass is 5.00 kg and the spring has a force constant of 1-00N/m.