Results 1 to 4 of 4

Math Help - The motion of a body falling in a viscous medium differential equation help (:

  1. #1
    Newbie
    Joined
    Jul 2013
    From
    New Zealand
    Posts
    3

    The motion of a body falling in a viscous medium differential equation help (:

    The motion of a body falling in a viscous medium may be described by the equation:

    m(dv/dt) = -bv-mg

    where m, g, b are positive constants. The initial conditions are v(0) = 0 and x(0) = 0.Determine the velocity v(t) and displacement x(t) for t < 0.

    Anyone able to help please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445

    Re: The motion of a body falling in a viscous medium differential equation help (:

    \displaystyle \begin{align*} m\,\frac{dv}{dt} &= -b\,v - m\,g \\ \frac{dv}{dt} &= -\frac{b}{m}\,v - g \\ \frac{dv}{dt} + \frac{b}{m}\,v &= -g \end{align*}

    This is now first-order linear, so solve using the Integrating Factor method.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2013
    From
    New Zealand
    Posts
    3

    Re: The motion of a body falling in a viscous medium differential equation help (:

    Ok so I can get to v(t)=(-gm/b)(1+e^(-bt/m)) (is this correct?)

    However, I am unsure now as to solve for x(t).

    Sorry I have not yet learnt how to use the proper math writing on here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445

    Re: The motion of a body falling in a viscous medium differential equation help (:

    I get \displaystyle \begin{align*} v = -\frac{g\,m}{b} \left( 1 - e^{-\frac{b}{m}\,t} \right) \end{align*}

    Surely you know that velocity is the derivative of displacement, or the other way, displacement is the antiderivative of velocity...
    Last edited by Prove It; July 20th 2013 at 08:10 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. falling body
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 25th 2010, 10:11 PM
  2. Motion equation of a free falling object, with air resistance
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 26th 2010, 05:20 AM
  3. Motion in a resisting medium
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 17th 2009, 05:35 AM
  4. Motion in a resisting medium
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: August 30th 2009, 08:37 PM
  5. The falling body
    Posted in the Calculus Forum
    Replies: 7
    Last Post: October 16th 2007, 04:05 PM

Search Tags


/mathhelpforum @mathhelpforum