1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Equation of motion coursework

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data

    I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with.

    I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper.

    2. Relevant equations

    I am assuming you find the deflection at the end of the beam as a result of the force P(t), which i think is

    However i am not sure where to go from here

    3. The attempt at a solution

    Thinking it may possibly be
    however i think i may need to add in stiffness somewhere else..

    Attached Files:

  2. jcsd
  3. Feb 23, 2009 #2
    Your simple model for the cantilever, looks OK, and it gives you the stiffness if you look at it properly. You have a deflection relation that is usually written as
    defl = P*L^3/(3*E*I)
    Now re-arrange that to read
    P = (3*E*I)/(L^3) * defl
    and from there you can see that the stiffness of this system is
    K = 3EI/L^3
    Now back to your equation of motion, which will look like
    m*xddot + c*xdot + K*x = F(t)
    where F(t) is whatever applied forcing function acts on the mass.

    See if that will get you going!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook