A magnetic compass has its needle, of mass 0.050 kg and length 4.0 cm, aligned with the horizontal component of Earth's magnetic field at a place where that component has the value Bh = 16μT. After the compass is given a momentary gentle shake, the needle oscillates with angular frequency w = 45 rad/s assuming that the needle is a uniform thin rod mounted at its center, find the magnitude of its magnetic dipole moment.