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Simple harmony

  1. Mar 23, 2005 #1
    I have two questions:

    #1.) The velocity of a simple harmonic oscillator is given by
    v=-7.22(26.0t) (mks units)

    If the mass is 0.29kg, what is the spring's potential energy at the time t=40.33?

    MY WORK:
    First I found k by using ω^2=k/mass. This equaled 196.04.

    I couldn't really figure out how I was supposed to derive aplitude (A) for that, So i figured since v=-Aω sin (ωt) that A =7.22/2.60.

    Then i took my (probably not right) amplitude and put it into U=.5kA^2cos^2(ωt).

    *This didn't work out, possibly because I can't figure out how to get the correct amplitude??

    #2.) A 0.28 kg mass is attached to a vertical spring with a spring constant 9.1 N/m and let fall. What is the amplitude of the resulting motion?

    MY WORK:
    Since its a vertical spring, i used the equation: y0=mg/k. When I got the y0, i figured this to be twice my aplitude, so i divided it by 2.

    *Wrong, again because I have issues with amplitude.

    Please help me!!
  2. jcsd
  3. Mar 24, 2005 #2
    This is not the equation of velocity in SHM. It is of the form v = kt, i.e. it describes motion at constant velocity.

    You are in the wrong track. It will be more feasible for you to use the law of conservation of Energy:

    [tex]PE_{G1} + PE_{E1} = PE_{G2} + PE_{E2}[/tex]
  4. Mar 24, 2005 #3
    I am still completely clueless as to how to get the Amplitude. If I could figure that out, the problem #1 would be much easier to work out. I figure you could use the time t given to get a numerical value for velocity, but how can I relate that to A with other knowns I have?

    I am not able to make sense of an equation in that form, and what exactly it means. Also, my professor isn't very willing to help with the students, so I have essentially no other resources.

    Any help at all would be immensly appreciated.
  5. Mar 26, 2005 #4
    As I said you cannot determine the amplitude A, given only the equation of velocity which is wrong (v = kt)! Try to revisit the question, or ask your professor about the correct equation of v(t), and post it here again. Good luck!
  6. Mar 26, 2005 #5
    If you know x(t) = Acos ωt (as you used it to get PE), why isn't your velocity, v(t) = -Aωsin ωt??
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