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!

What is the amplitude of sinusoidal motion?

  1. Feb 10, 2012 #1

    Aar

    User Avatar

    1. The problem statement, all variables and given/known data

    An object with mass 0.222 kg is hung on a spring whose spring constant is 86.4 N/m. The object is subject to a resistive force given by -bv, where v is its velocity. The ratio of the damped frequency to the undamped (natural) frequency) is 0.886. If this system is subjected to a sinusoidal driving force given by

    F(t)=(8.75 N)sin(0.901ωo t) ,

    what is the (steady-state) amplitude (in cm) of the resulting sinusoidal motion

    2. Relevant equations

    A = A[itex]_{o}[/itex]/[itex]sqrt{( (1-r^2)^2 + (r^2/q^2) )}[/itex]

    r = w[itex]_{d}[/itex]/w[itex]_{o}[/itex]

    Q = (w[itex]_{o}[/itex]*M)/b

    A[itex]_{0}[/itex] = Fm/k

    F(t) = (Fm)cos(w[itex]_{d}[/itex]*t)

    w[itex]_{d}[/itex] = [itex]\sqrt{w_{o}-(b/2m)^2}[/itex]

    w^2 = k/m

    3. The attempt at a solution

    this is what I attempted initially and obtained an answer that was correct however in attempting other questions with different numbers the answers which I obtained were not correct. I am wondering if it was coincidental that the initial answer I obtained worked out to be a correct value or if it was the correct method and the program which I submitted the answer in was not registering the answers correctly.

    initially solve for w[itex]_{0}[/itex] w[itex]_{d}[/itex] than obtain b

    w[itex]_{0}[/itex] = [itex]\sqrt{86.4/0.222}[/itex] = 19.73

    w[itex]_{d}[/itex] = w[itex]_{0}[/itex]*0.866 = 17.47

    b = 2/m * [itex]\sqrt{(19.73)^2 - (17.47)^2}[/itex] = 4.0615

    q = 19.73*0.222/4.0615 = 1.0783

    A[itex]_{o}[/itex] = 8.75/86.4 = 0.10127

    A = 0.10127/[itex]sqrt{( (1-0.866^2)^2 + (0.866^2/1.0783^2) )}[/itex] = 0.1192 m

    convert to cm and the answer obtained is = 11.92cm

    my uncertainty is wether or not the value in the sinusoidal driving force equation if the 0.901w[itex]_{o}[/itex] has any effect on determining w[itex]_{d}[/itex].

    thanks for any help
     
    Last edited: Feb 10, 2012
  2. jcsd
  3. Feb 11, 2012 #2
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is the amplitude of sinusoidal motion?
  1. Sinusoidal Motion (Replies: 10)

Loading...