Why does a pendulum have a constant period when the angle is small?

The key is:
F=mgsin(theta)cos(theta) ~ mg * theta
F=-kx=-L*theta*k
T=2*pi sqrt(m/k)


More:
http://dev.physicslab.org/Document.aspx?doctype=3&filename=OscillatoryMotion_PendulumSHM.xml