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Spring and Amplitude Problem

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    A mass is attached to the wall by a spring of constant k. When the spring is at its natural length, the mass is given a certain initial velocity, resulting in oscillations of amplitude A. If the spring is replaced by a spring of constant 2k, and the mass is given the same initial velocity, what is the amplitude of the resulting oscillation?


    2. Relevant equations
    E = 1/2mv^2 + 1/2kx^2 = 1/2kA^2

    3. The attempt at a solution
    I am not quite sure what equation to really apply here, or how to approach the problem to find the amplitude. The answer is 1/(√2).
     
  2. jcsd
  3. Jan 27, 2013 #2

    ehild

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    The velocity is given when the spring is relaxed. So you get the amplitude from the equation 1/2mv^2 =1/2kA^2

    Double the spring constant: k'=2k. Now you have the equation for the new amplitude A'. 1/2mv^2 =1/2 k' A'^2 . V is the same, so 1/2kA^2= 1/2 k' A'^2. How are A and A' related?


    ehild
     
  4. Jan 27, 2013 #3
    well, by substituting k' = 2k,
    you end up with A^2 = 2 (A')^2
     
  5. Jan 27, 2013 #4

    ehild

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    Isolate A'.

    ehild
     
  6. Jan 27, 2013 #5
    You end up with 1/√2 A, which is the correct answer.
    Thank you very much for the help!
     
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