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!

Damped Oscillator

  1. Feb 6, 2014 #1
    Hey guys I'm new to the forum and having a little trouble with this conceptual problem.

    1. A block of mass m is connected to a spring, the other end of which is fixed. There is also a viscous damping mechanism. The following observations have been made of this system:

    i) If the block is pushed horizontally with a force equal to mg, the static compression of the spring is equal to h

    ii) The viscous resistive force is equal to mg as the block moves with a speed u.


    a) Write the differential equation governing horizontal oscillations of the mass in terms of m, g, h and u.

    b) for the particular case of u = 3√gh, what is the angular frequency of the damped oscillations?


    2. Relevant equations:

    mx'' + λx' + kx = 0


    3. The attempt at a solution:

    F = mg = -kh (x = h)

    F = mg = -λu for x' = u

    At this point I'm somewhat lost and not sure what they're looking for. If the viscous force = mg at velocity u, how can you translate that into a differential equation that covers all velocities of the mass? Any help would be greatly appreciated
     
  2. jcsd
  3. Feb 7, 2014 #2
    Can you obtain express ##k## and ##\lambda## from the conditions given?
     
  4. Feb 7, 2014 #3
    Oh, you're saying to set k = -(mg)/h and lambda = -(mg)/u and plug that into the diffeq? I don't know why that never occurred to me, thanks a lot for the suggestion!
     
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: Damped Oscillator
  1. Damped oscillations (Replies: 3)

Loading...