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: Block and Spring (Simple Harmonic Motion Problem)

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data

    At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched?

    2. Relevant equations

    phi=phase angle
    angular frequency= sqrt(k/m)=w
    x(t)=Acos(wt+phi)

    3. The attempt at a solution

    After working through the givens, I got my equation for the harmonic motion to be
    x(t) = 0.66 cos (3.4987t - 2pi/3)
    Where the angular frequency is sqrt(61.2/5)=3.4987, I got the amplitude from conservation of energy to be .6607 meters and the phase angle is -2pi/3.

    The next step, if I am not mistaken, is to solve for when the spring is at its equilibrium position, or when x(t1)=0. Here are the steps for what I did...

    0=0.6607 cos (3.4987t - 2pi/3)
    0=cos(3.4987t - 2pi/3)
    cos-1(0)=3.4987t - 2pi/3
    pi/2= 3.4987t -2pi/3
    7pi/6=3.4987t
    t=1.0476 seconds

    which, according to the homework website, is not correct! Can anyone see where I made my mistake? Thank you!!
     
  2. jcsd
  3. Apr 14, 2010 #2
    I think probably since the motion is starting at t=0, then x(t) is better to be written as A cos(wt) , (im not really sure) .. but i think it is something like that ..

    i have a question for you, why did you take phi = -2pi/3
     
  4. Apr 14, 2010 #3

    ehild

    User Avatar
    Homework Helper

    3.4987t - 2pi/3 is sooner -pi/2 than pi/2.

    ehild
     
  5. Apr 14, 2010 #4
    I figured out what I did wrong in this situation... cos-1(0) could be either pi/2 or -pi/2, and because the motion is coming to the end of a complete cycle I should have used -pi/2.

    To answer your question, I determined the phase shift=phi by solving the position equation. I knew at t=0, x(t)= -.33 meters, so you just solve x(t) = A cos (wt + f) for f, and I got -2pi/3.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook