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Find the total energy of the system

  1. Sep 3, 2007 #1
    1. The problem statement, all variables and given/known data

    A 50.0 gram object, connected to a spring with a force constant of 35.0 N/m oscillates on
    a horizontal, frictionless surface with an amplitude of 4.00 cm.
    Find: a) The total energy of the system.
    b) The speed of the object when the position is 1.00 cm
    c) The Kinetic Energy and the Potential Energy when the
    position is 3.00 cm.


    2. Relevant equations
    x(t)=Acos(wt+phi)
    v(t)=-[wA]sin(wt+phi)
    E=U+K
    U=1/2kA^2
    K=1/2mv^2

    3. The attempt at a solution
    i guess what i am having trouble with is solving for the kinetic energy in part A. i know that i can substitute the v(t) equation for v but where am i getting the phase constant, or the time components? or can i just ignore them and assume that x=A and therefore K=0 so total energy would be just 1/2kA^2. as for part B my method is that i want to solve for the phase constant in the x(t) equation first and then plug that into my velcity equation but what do i do about the time variable? then using that phase constant i found i am going to find part C. do these methods work? and please advise on part A thanks.
     
    Last edited: Sep 3, 2007
  2. jcsd
  3. Sep 3, 2007 #2
    So, you do have the right information for getting the right phase constant. (As a quick note, make sure you watch the units that are given.) As of now I'm going to assume this is a calculus based course, and that if you are given a maximum for a given function (position in your case) you know what to do to find that maximum.

    You are correct about how you can just plug in whatever you find though. For part b you will want to know the time to plug into the velocity equation, any ideas on how to find that? Part c will function similarly.
     
  4. Sep 3, 2007 #3
    how do i find the phase constant (phi)? is it pi/2?
     
  5. Sep 3, 2007 #4
    The phase constant is actually arbitrary in this case, unless you are given some initial conditions you didn't post. Do you see why?

    How will you find A? What do you get for your equation x(t)?
     
  6. Sep 3, 2007 #5
    amplitude is provided and = 4, can i really just ignore phi? my x(t) equation is then just x(t)=4cos(.837t)
     
  7. Sep 3, 2007 #6
    Yeah, the problem doesn't say anything about initial conditions, so you might as well just pick anything along the sine or cosine waveform. This makes sense because the question keeps asking about energies at certain positions, which does not explicitly depend on time in a conservative system.

    Watch your units, check the eqn again.
     
  8. Sep 3, 2007 #7
    yea i see what u mean, i'm mixig cm with m, and N and grams. thanks for the help
     
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