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!

Spring Problem, Differential Equations

  1. Oct 30, 2014 #1
    1. The problem statement, all variables and given/known data
    A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s2.

    2. Relevant equations

    3. The attempt at a solution

    I solve for k and get 64, and solve for the mass and get 32/64, so my differential equation is 0.5y'' + 2y' + 64y = 0, I solve for r and get c1*e^(-2t)*cos(2t*sqrt(31)) + c2*e^(-2t)*sin(2t*sqrt(31))

    My initial position is 0, so y(0) = 0, and my initial velocity is -2, so y'(0) = -2

    So substituting, I get

    0 = c1*e^0*cos(0) + c2*sin(0)

    0 = c1

    Now for y',

    y' = -c1*e^(-2t)*sin(2t*sqrt(31))*2sqrt(31)) + -2c1*e^(-2t)*cos(2t*sqrt(31)) + c2*e^(-2t)*cos(2t*sqrt(31))*2sqrt(31) - 2*c2*e^(-2t)*sin(2t*sqrt(31))

    -2 = -c1*e(0)*0 - 2c1e^(0)*cos(0) + c2*e^(0)*cos(0)*2sqrt(31) - 2*c2*e^(0)*sin(0))

    -2 = -2c1 + c2*2sqrt(31)

    But c1 is 0, so -2 = c2*2sqrt(31), and so c2 = -1/sqrt(31)

    So my final equation is -1*e^(-2t)*sin(2t*sqrt(31))/sqrt(31)

    But when I pick that as an option, the computer marks it wrong. I see some options with a 12sqrt(31) on the bottom, but I don't think that's it.
  2. jcsd
  3. Oct 30, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You have to be careful with units here. If the initial velocity is -2 in/s, then you can't just blindly plug y'(0) = 2 into your equation, because the damping constant was given as 2 lb-s/ft. The initial velocity should be -2/12 ft/s, to convert in/sec to ft/sec.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted