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!

Vibration and Waves: Springs

  1. Jan 27, 2008 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    For a mass m hung vertically from a spring with spring constant s, the restoring Force is F=-sx where x is the displacement from equilibrium.

    a)What are the periods of the two harmonic oscillators i) and ii).
    b)Assuming eaqch oscillator is moving with the same Amplitude A which has the greater total energy of oscillation and by what factor is it greater?

    2. Relevant equations

    F=-sx
    omega=(s/m)^1/2


    3. The attempt at a solution

    I just don't really know if there is any difference between i) and ii) but there has to be since all the following questions build up on it. But how can I prove that mathematically?
     
    Last edited: Jan 27, 2008
  2. jcsd
  3. Jan 27, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The first thing you need to do is figure out the effective spring constant of those two spring configurations. Analyze how the force depends on the displacement: F = k' x.
     
  4. Jan 27, 2008 #3
    Yes, I got it now.
    The series one adds as in series therefore 1/stotal=1/s1+1/s2 and the other one like parallel therefore stotal=s1+s2.
    Wouldn't have thought this because experience actually told me that it shouldn't be so much of a difference... I mean ii) has 4 times more total energy than i).

    But now I'm stuck at a new problem.

    A damped oscillator of mass m=1,6 kg and spring constant s=20N/m
    has a damped frequency omega' htat is 99% of the undamped frequency omega.

    a) What is the damping constant r?
    Attempt:
    As far as I know \omega ' = \sqrt{ \omega ^2 - \frac{b}{2m}}
    But were to go from here?
    edith: Ok, got that now.

    therefore b = (0.99^2-1)*(s/m)*(2m)*(-1) which in this case is 0.796.

    b)What is the Q of the system?
    Attempt:
    Q=\sqrt{mass * Spring constant} / r
    But again I would have to find r from a) which I can't really figure out.
    Ok, with a) answered I got Q to beeing 7.1066

    c) Confirm that the system is lightly damped.
    I think a system is lightly damped if omega' is about euqal to omega, but this can't really be the answer here. Because thats whats stated anyways since 99% is "about equal" isn't it?

    d) What new damping constant r_{new} is required to make the system critically damped?
    Again, I couldn't find any definition on the web or in my notes what critically damped means.

    f)Using r_{new} calculate the displacement at t=1s given that the displacement is zero and the velocity is 5 ms^-1 at t=0.
    No clue here.

    Note:How can I insert Tex in this forum?
     
    Last edited: Jan 27, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?