Pivoting planks.
Classical Mechanics
Level
3
A horizontal plank of mass \(m\) and length \(L\) is pivoted at one end and is attached by a spring of force constant \(k\) at the other end.
A small mass M is glued at the free end of the plank supported by the spring.
When the plank is displaced upward by a small angle of \(\theta\) from its equilibrium position and released, it undergoes simple harmonic oscillations at angular frequency expressed as \[\omega = \sqrt{\dfrac{ak}{m + bM}}.\] What is \(a + b?\)
by
Vijay Simha