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Springs Double

  1. Dec 19, 2013 #1
    1. The problem statement, all variables and given/known data
    You have two springs with spring constants k_1 = 10 and k_2 = 20 vertically attached to a wall, and a mass of mass 3.00kg is hung from it. Find the period of oscillation.


    ----------------
    ||
    || <-- first spring, k_1 = 10
    ||
    --
    ||
    || <== second spring, k_2 = 20
    ||
    {} <== mass 3.00kg

    2. Relevant equations

    F=-kx
    T = 2pi/omega


    3. The attempt at a solution


    Consider the second spring. We have:
    [itex] F=-kx \implies 3(-9.8) = -(20)(x) \implies x = 1.47 [/itex]

    Now the second spring undergoes a displacement of:

    [itex] F=-kx \implies 3(-9.8) = -(10)x \implies x = 2.94 [/itex].

    So k effective is:

    [itex] F = -k (x_1+x_2) \implies 3(9.8) = k(2.94+1.47) \implies k = 4.41[/itex]

    From here, i just found [itex]\omega[/itex] by using [itex]\omega =\sqrt{k}{m}[/itex]. and the period was easy from there.

    Is the first part of my solution correct? Im having trouble visualizing it.
     
  2. jcsd
  3. Dec 19, 2013 #2

    Doc Al

    User Avatar

    Staff: Mentor

    So far so good.

    4.41 is the total displacement, not the spring constant. Solve for the effective spring constant.
     
  4. Dec 19, 2013 #3
    oops i meant 6.666. Thank you.

    A follow up question to this has the same springs, except oriented like this:

    -------------------
    || ||
    || ||
    || ||
    || ||
    ------
    | {} |
    ------


    With the springs parallel. How would you solve this? I am still not convinced that there is a solution (to me, the "block" will be tilted).
     
  5. Dec 19, 2013 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Assume the system is constrained so that the springs get the same displacement.
     
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