Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Forced vibrations w/ damping problem

  1. Mar 10, 2005 #1


    User Avatar

    A spring is stretched 6 inches by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec/ft and is acted on by an external force of 4cos(2t) lb.

    a) Determine the steady-state response of this system
    b) If the given mass is replaced by a mass m, determine the value of m for which the amplitude of the steady-state response is maximum.

    I got part a but didnt get part b.... Im not sure where to start... can anyone tell me how to start it? or any tips?

    ps the answer to a is U(t) = (8/901)(30cos(2t)+sin(2t)) ft

  2. jcsd
  3. Mar 11, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Write the expression for U(t) in terms of m (do not substitute m=8 lb).

    Find the amplitude A(m), to be half the difference between the minimal and maximal values of U(t). The minima and maxima can be found from dU(t)/dt = 0.

    Maximize the amplitude by setting dA(m)/dm = 0.
  4. Mar 11, 2005 #3


    User Avatar

    I actually got it already. Sorry about it but thanks anyways. it was such a simple calculus problem.................
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook