1. Not finding help here? Sign up for a free 30min 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!

Homogenous ODE problem

  1. Oct 20, 2012 #1
    Hi all,

    I'm struggling with this question - I don't really know where to start. So far I have tried putting arbitrary values for 'a' into a quadratic auxiliary equation but using wolfram to calculate the roots gives me complex conjugates that I cant remember a thing about. Question as follows:

    A body of mass 'm' kg attached to a spring moves with friction. The motion is described by the second Newton's law:

    m(t).y" + a(t).y' + ky = 0

    Where y is the body displacement in m, t is the time in s, a > 0 is the friction coefficient in kg/s and k is the spring constant in kg/s^2. Assuming m=1kg and k=4kg/s^2 find;

    A) what is the range of values of a for which the body moves (i) with oscillations, (ii) without oscillation?

    B) Find the general solution for any a<4 (Your solution should be a formula depending on the parameter a.) Proof that it follows from the solution obtained that the body slows down to a virtually rest state at large time (ie when t > infinity)?

    C) find the particular solution for a=4 subject to the initial conditions y(0)=0, dy/dt= 1m/s at t=0. Plot this solution and determine the largest displacement of the mass usIng calculus.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Homogenous ODE problem
  1. ODE Problem (Replies: 0)

Loading...