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!

Problem of harmonic motion

  1. Jun 29, 2016 #1
    1. The problem statement, all variables and given/known data
    A particle with mass m is undergoing with harmonic motion with a period T, we introduce an external force F proportional to velocity v so that F= -bv with b a constant and we assume that the particle continues to oscillate how does the period change?

    2. Relevant equations F= m a ; v'= a; x'= v; x''= a


    3. The attempt at a solution

    So my idea was creating the differential equation of the motion:

    Before the external force to be applied :

    m x" + k x= 0 (there, must be a force F=-kx even if the problem doesn't mention it so that the harmonic motion exists before the application of the external force) so T= 2 pi (m/k)^0.5


    After the force:

    mx'' + b x' + k x= 0 , the problem is that this equation has not as a solution a function like this x (t)= A cos ( wt + phi) but a linear combination of exponential function so I can't figure out what the period is... (to solve the equation is used wolfram alpha and it doesn't give me a sinusoidal function)

    Please help me this problem is freaking me out
     
  2. jcsd
  3. Jun 29, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    It's an elementary problem in differential equation, called damped harmonic motion. See this link about a way to solve such kind of problem. Note that since the problem assumes the particle to continue undergoing oscillation, this problem implies the underdamped solution.
     
  4. Jun 30, 2016 #3
    The relation in the link doesn't give me info about the new period of oscillation, because the solution is not a sinusoidal function but expo, how do I get it?
     
  5. Jun 30, 2016 #4
    Ok, i found it, thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Problem of harmonic motion
Loading...