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: Mass-spring-dampened system

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A mass-spring-dampener system is applied a force [itex]mg[/itex] and is immediatly removed, setting the system in motion. The system is constantly applied force [itex]Mg[/itex] and is static at [itex]y=y_0[/itex].
    Find a formula for both [itex]A[/itex] and [itex]\phi[/itex]


    2. Relevant equations

    [itex]\ddot{y}+2\delta\dot{y}+w_0^2y=0[/itex]
    [itex]\frac{2\pi}{w_0}=T_0[/itex]
    [itex]\delta = \frac{3}{5}w_0[/itex]
    [itex]F_f=-b\dot{y}[/itex]
    [itex]Mg=ky_0[/itex]

    3. The attempt at a solution

    from this i find [itex]k[/itex] and [itex]b[/itex]. No problem, not part of my question.

    when the force is applied, the system 'moves' in y direction and is set in motion, given function:

    [itex]y(t)=Ae^{-\delta t}cos\left(w_d t+\phi\right)[/itex]
    [itex]w_d=\sqrt{w_0^2+\delta^2}[/itex]

    I'm to find [itex]A[/itex] and [itex]\phi[/itex]

    my try:

    I understand [itex]\dot{y}(0)=0[/itex] gives:
    [itex]\dot{y}=-\delta Ae^{-\delta t}cos(w_d t+\phi)-w_d A e^{-\delta t}sin(w_d t + \phi)[/itex]
    gives:
    [itex]\phi=\arctan{\frac{-\delta}{w_d}}[/itex]

    however i do not find a substitute for [itex]y(0)[/itex]. The solution says [itex]y(0)=\frac{m}{M}y_0[/itex], but i don't see the logic in that at all

    Sorry if its a bit caotic, this is only part of the assignment. ask and i will provide!
     
  2. jcsd
  3. Nov 15, 2012 #2
    nvm, found the solution
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...