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A mass between two springs-simple harmonic motion

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m.

    This is what the the picture looks like in words.
    From left to the right, these are the objects.

    Wall, spring 1, 4kg mass, spring 2, wall

    1. How much is spring 2 stretched?
    2. What is the potential energy stored in each spring?
    3. Taken as a simple harmonic motion system, what is the potential energy stored in the system



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations
    F=ma
    Restorative force=-kx perhaps?



    3. The attempt at a solution
    1. F=-kx=-40(4)=-160N
    160=-kx=-60x
    x=-8/3 meters
    8/3 meters to the left?

    2. PE=0.5kx^2=0.5(40)(4)^2=320J in Spring 1
    PE=0.4kx^2=0.5(60)(-8/3)^2=640/3 J in Spring 2

    3. 320+(640/3)=1660/3 J

    I'm very unsure about these answers. To be honest, I don't understand the questions.
     
    Last edited: Apr 11, 2012
  2. jcsd
  3. Apr 11, 2012 #2
    Hello cnputhur, welcome to PF.

    Your solution to the first question is the correct magnitude. However your minus signs may have gone awry. Try labeling the forces in future to help with these things ( a diagram will then make it very clear which way it must go).

    And for question 2?...
     
  4. Apr 11, 2012 #3
    f=kx. -ve sign only indicates it is in the opp. direction.
    about energy, spring p.e. =1/2kx^2
     
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