{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture_21 (dragged)

lecture_21 (dragged) - MA 36600 LECTURE NOTES FRIDAY MARCH...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 36600 LECTURE NOTES: FRIDAY, MARCH 6 Mechanical and Electrical Vibrations Hooke’s Law. Say that we have a mass m which is attached to a spring. Consider four forces on the mass m : Gravity: Newton’s Law of Gravity states that F g = m g . Restoring Force: Hooke’s Law states that F s = k ( L + u ) for some positive constant k . Damping: Say that the mass is in a viscous fluid, one which gives a type of damping. For example, the mass may be a ff ected by air resistance, or the mass may be in a liquid. Then the force of damping is proportional to the velocity i.e., F d = γ u for some positive constant γ . External: Say that the mass is acted upon by an outside mechanical force. We simply write this as F e = F ( t ) for some function. Newton’s Second Law of Motion states that F = m a . That is, m u + γ u + k u = F ( t ) . Hence the position u = u ( t ) satisfies a linear second order di ff erential equation. Note that in general, if we have an equation in the form a y + b y + c y = f ( t ) where a , b , and c are constants, we identify m
Image of page 1
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