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!

Calculate the z position of the particle as a function of time.

  1. Feb 25, 2014 #1
    1. A particle of mass m is suspended from the ceiling by a spring with constant K and relaxed length initial lo, whose mass is negligible. The particle is released at rest with the spring relaxed. Taking the Oz axis directed vertically downward, with the origin on the roof, calculate the z position of the particle as a function of time.



    2. Relevant equations
    x=[Acos(wt+phi)


    3. I know that the net force is given by F(net)=-kx+P where F(net) it will be d^2x/dt^2, so the expression takes the form. m*d^2x/dt^2=-kx+mg.

    How we know that d^2x/dt^2=-w^2x, So m(-w^2x)=-kL(o)+mg, So -w^2*x=-kL(o)/m+mg/m

    x=[Acos(wt+phi)

    -w^2[Acos(wt+phi)= -9kL(o)/m+mg/m) We know that w=sqrt(k/m)

    -w^2[Acos(sqrt(k/m)*t+phi)= -(kL(o)/m+mg/m)

    So help me to know if Am I right or not about the equation.
     
    Last edited by a moderator: Apr 28, 2014
  2. jcsd
  3. Feb 26, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The problem wants the z position of the particle as function of time. The z axis is oriented vertically downward. So write the differential equation in therms of z.
    The differential equation contains a constant term mg, in addition of the Hook force, so the z(t) function is not a simple cosine function. Solve the equation and fit it to the initial conditions.

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted