a$.$ A microcantilever with stiffness $0\mathrm{.}03200$ N m$1$ adsorbs a mass of $2\mathrm{.}1001012$ kg at its free end, where a region has been created for selective adsorption of species from solution. At a temperature of $37$C$,$ is the static deflection caused by the adsorption detectable beyond the thermal motion of the system? Assume Boltzmann$$s constant to be $1\mathrm{.}3811023$ J K$1$ and the acceleration due to gravity to be $9\mathrm{.}810$ m s$2.$

b$.$ An alternative MEMS sensor is considered: a microcantilever with resonant frequency $185\mathrm{.}0$ kHz and stiffness $20\mathrm{.}00$ N m$1.$ Calculate the change in resonant frequency that will occur when a mass of $2\mathrm{.}1001012$ kg adsorbs onto the cantilever. Assume that the stiffness remains constant.