Question

A uniform meter stick of mass M is pivoted on a hinge at one end and held horizontal by a spring with spring constant k attached at the other end. If the stick oscillates up and down slightly, what is its frequency? [Hint: Write a torque equation about the hinge.]

Answer 1

if the stick is displaced x at the spring end
restoring force = - kx

without spring attached to the stick, equivalent mass m at the end of stick
mg * L = Mg * L/2
m = M/2

net force at the end of stick
= m d^2 x / dt^2 = - kx
d^2 x / dt^2 = - kx /m
= - (k/m) x
= - (2k/M) x
angular speed
= sq root [ 2k/M]
= 2 pi *frq
frequency = [1 / 2pi] sq root [2k/M]