  We present the coupled oscillator: a new mechanism for signal amplification
with widespread application in metrology. We introduce the mechanical theory of
this framework, and support it by way of simulations. We present a particular
implementation of coupled oscillators: a microelectromechanical system (MEMS)
that uses one large (~100mm) N52 magnet coupled magnetically to a small
(~0.25mm), oscillating N52 magnet, providing a force resolution of 200zN
measured over 1s in a noiseless environment. We show that the same system is
able to resolve magnetic gradients of 130aT/cm at a single point (within
500um). This technology therefore has the potential to revolutionize force and
magnetic gradient sensing, including high-impact areas such cardiac and brain
imaging.
