Answer Happy

= #10. (10 pts) Harmonic oscillator: a. A harmonic oscillator with spring constant k, and mass, m, loses 5 quanta of energy, leading to the emission of a phonon. If the oscillator is a bonded atom with k = 25 N/m and m = 8 x 10-26 kg, and we use a photon to excite resonantly the oscillator, what is the frequency (Hz) of this photon? (Note: the energy of the photon is the same with the energy of the phonon) b. A cantilever beam has length, L = 200 um; width, w = 100 um; thickness, t = 500 nm; density, p = 2330 kg/m; damping coefficient, b = 3 x 10°Ns/m; and modulus of elasticity, Em = 1.3 x 10 N/m? In this micro-electro-mechanical (MEMS) device, the spring constant, k, of a rectangular cantilever beam is given by: k=(Ext)/(4L) What is the beam's damped resonance frequency, fres (Hz)? (Do not forget: met = 0.24*m for a cantilever beam in the question for damped resonance frequency). What is the quality factor? Can we detect a mass of 50 pg (picogram) added to the cantilever beam? (Note: 1 Pg - 10 kg)?