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Amplitude of a spring

  1. May 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Lets say I have a spring, resting at a length x at t = 0 seconds, with a spring constant k, and at the end is attached with a block with mass m. I give the block a velocity v in the -x direction.

    Now I'm asked to find the Amplitude.

    2. Relevant equations


    3. The attempt at a solution

    Here, I'm thinking, KEmax = PEmax = 1/2 m v2 = 1/2 k A2

    since the highest velocity is the initial 'push' i give it, is it safe to say I have every variable to solve for A(amplitude)?
     
  2. jcsd
  3. May 18, 2015 #2

    berkeman

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    Staff: Mentor

    Looks good to me so far... :smile:
     
  4. May 18, 2015 #3
    so when is 1/2 k A2 = 1/2 mv2 + 1/2 k x2?

    is that when you don't know the max velocity? is that when you know a given velocity and distance at a given time?
     
  5. May 18, 2015 #4

    berkeman

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    This looks correct for when v = the velocity at zero displacement.

    This is confusing. Why are you adding the two terms on the RHS?
     
  6. May 18, 2015 #5
    I think to add up the total energy at a given time so KEmax =PEmax = 1/2 k x2 at a given time + 1/2 mv2 at a given time

    I could be wrong though
     
  7. May 18, 2015 #6

    berkeman

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    That does look correct, but you should add subscripts to the velocity v to make it clear what you mean in each case. KE max is at zero displacement, and PE max is at maximum displacement. And KE + PE at any given point is equal to KE max or PE max.
     
  8. May 18, 2015 #7
    KEmax =PEmax = 1/2 k x^2 at a given time + 1/2 mv^2 at a given time = 1/2 k A 2

    then I can solve for Amplitude, if I'm given a time where displacement isn't 0

    correct?
     
  9. May 18, 2015 #8

    berkeman

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    Not quite.

    KEmax = PEmax = 1/2 k A^2 = 1/2 m v(x=0)^2. At any given time KEmax = PEmax = 1/2 k x^2 + 1/2 m v^2

    Where A = max amplitude.
     
  10. May 18, 2015 #9
    isn't that what i typed out?
     
  11. May 18, 2015 #10

    berkeman

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    Not the way I read it. I bolded the things I changed and added.
     
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