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!

Forced vibration with decreasing force amplitude

  1. Nov 21, 2011 #1
    I have a damped forced vibration problem. Most problems I have dealt with have a constant amplitude sinusoidal force such as F_0sin(wt). Lets say you have an applied force that decreases each second at a constant rate over 11 seconds. It looks like this:

    F=0.5*[(11-t)sin(2*pi*t)+(11-t)]; (0<= t >=11)

    The graph of this force has been attached.

    The system is also critically damped so the system's differential equation is:

    m[d^2/dt^2](x) + c(dx/dt) +kx = 0.5*[(11-t)sin(2*pi*t)+(11-t)]

    From here i'm not too sure how to proceed. Normally with forced vibration the solution would include both a complimentary and particlular soluntion since it is a nonhomogenous linear second order differential equation. So

    x = x_c + x_p

    If the force had a constant magnitude (steady state vibration) and assuming critical damping x_c would look like:

    x_c=(A+B*t)e^(-W_n*t)

    but since the vibration is not steady state does this equation hold true? I assume it does only because the complimentary solution is found by setting the force to zero and assuming only free vibration. A and B are then found using the initial conditions where:

    A= x_c(0) or is it A=x(0)
    B=Dx(0)/dt + w_n*x(0)

    Then x_p needs to be found and this im having trouble with. how would one solve this part of the differential? The variables such as k and m should be left as variables. Do i need an equation solver that can handle solving with variables such as Maple?
     

    Attached Files:

  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?
Draft saved Draft deleted



Similar Discussions: Forced vibration with decreasing force amplitude
  1. Forced vibration (Replies: 2)

Loading...