A horizontal plank of mass m and length L is pivoted at one end The planks 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 theta from its horizontal equilibrium position and released (a) Show that it moves with simple harmonic motion with an angular frequency w radic 3k m (b) Evaluate the frequency if the mass is 5 00 kg and the spring has a force constant of 1 00N m Pivot Figure P15 61

Question: A horizontal plank of mass m and length L is pivoted at one end. The planks other end is supported by a spring of force

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.

A horizontal plank of mass m and length L

Pivot Figure P15.61

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