hw_6 - ME 141A Intro to Nanotechnology Due HOMEWORK#6...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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.”
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern