hw_6 - ME 141A Intro to Nanotechnology Due: 2/23/2009...

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ME 141A Intro to Nanotechnology Due: 2/23/2009 1 HOMEWORK #6 Problem 5.7 in book A silicon cantilever beam is 300 μ m long, 100 μ m wide and 6 μ m thick. Silicon’s modulus of elasticity is 110 GPa; its density is 2330 kg/m 3 . (a) Determine the spring constant, k , of this beam. (b) Determine the natural frequency in radians per second. (c) Express your answer from part (b) in hertz. Problem 5.13 in book A cantilever beam has length, l=100 μ m; width, w=40 μ m ; thickness, t= 5 μ m ; modulus of elasticity, E M =100 GPa; density, ρ = 2000 kg/m 3 ; and damping coefficient , b=10 - 7 N* s/m . (a) What is the beam’s damped natural frequency, f (Hz)? (Do not forget, for a cantilever beam m eff =0.24 m in the equation for damped natural frequency.) (b) What is its quality factor? (c) A periodically varying driving force with F 0 =10 nN acts on the beam. Plot the amplitude, A, of the beam’s oscillation as a function of the drive frequency, F drive . Include F d on the graph so that the resonance peak is visable. (d) On the same graph, plot the amplitude if the damping coefficient quadruples. Label this curve “extra damping.” (e) On the same graph, plot the amplitude if, instead, the effective mass of the beam increases by 500 femtograms. Label this curve “extra mass.”
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This note was uploaded on 03/23/2009 for the course ME 141A taught by Professor Pennathur during the Winter '09 term at UCSB.

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hw_6 - ME 141A Intro to Nanotechnology Due: 2/23/2009...

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