A MEMS resonator has natural frequency

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Nonlinear dynamics and chaos · Nonlinear dynamics and chaos

Modes, Packets and Media, Ch Driven and pumped nonlinear oscillators and the route to chaos

Problem

A MEMS resonator has natural frequency ω0=1.00×105 rad s−1\omega_0=1.00\times10^5\,\mathrm{rad\,s^{-1}}, quality factor Q=2000Q=2000 and cubic nonlinearity ε=1.00×1015 s−2 m−2\varepsilon=1.00\times10^{15}\,\mathrm{s^{-2}\,m^{-2}}. ((a)) Find its critical amplitude AcA_{\rm c}, the amplitude at which the response curve first has a vertical tangent (the onset of triple-valued response). ((b)) Find the critical drive F0c/mF_{0\rm c}/m that must not be exceeded if the resonator is to stay in its single-valued, hysteresis-free operating range.

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