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: Given a harmonic oscillator with mass m, and spring constant

  1. Mar 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Given a harmonic oscillator with mass m, and spring constant k, is subject to damping force F= cdx/dt and driven by an external force of the form F[ext]= FoSin(wt).

    A) Find the steady state solution.
    B) Find the amplitude and the phase.

    2. Relevant equations

    the steady state is usually in the form of X(t)= Acos(wt+Φ)

    3. The attempt at a solution\
    So i came up with this equation for the Fnet force.

    F[net]= -kx+c(dx/dt)+FoSin(wt)
  2. jcsd
  3. Mar 29, 2015 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    What should be the sign of your c dx/dt term? Think about it.
  4. Mar 29, 2015 #3
    The sign of my dx/dt term should be X(dot)
    or are you saying it should be negative instead of positive?

    Once I have that should I move all the signs to the other side
  5. Mar 29, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Hello star,

    Rudy wants you to think about the sign: a + or a -
    In other words: if dx/dt > 0, which way does a damping force point ?

    Usually we take the damping coefficient (in your case c) as a positive value and therefore we need a + or - sign in the equation of motion to let the force point the correct way.
  6. Mar 29, 2015 #5
    When dx/dt >0 then the force has displacement to the right

    Well I rearranged the equation of motion into

    which then turns into X(doubledot)= -Wo^2X-2γx(dot)+(Fo/m)Sin(wt)

    Then I balanced the equation by bringing everything to the otherside
    and using known equation for the angular frequence Wo=√(k/m) and C = 2γm
    we receive

    X(doubledot)= -Wo^2X-2γx(dot)+(Fo/m)Sin(wt)

    Then in order to find the steady state solution we must assume the gamma is equal to 0 but why do we consider gamma as equal to zero?
  7. Mar 29, 2015 #6


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    $$\ddot x + 2\gamma\;\dot x + \omega_0^2\; x = {F_0\over m} \sin(\omega t)$$ looks good to me. But the
    does not. As you say: "why consider ##\gamma = 0 ## ?". What is your perception of this steady state solution you are looking for ?

    is indeed correct. What it tells you (should tell you) is that after an initial reponse that dampens out (-- thanks to the non-zero gamma! --), the oscillator will oscillate with the period of the driving force and with a certain amplitude; there will also be (or may be) a phase difference between the driving force and the oscillator.

    That the given form is actually a solution can be shown by substituting it in the equation. That will also help you on your way to find A and ##\phi##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted