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Mass-Spring System Equation

  1. Sep 26, 2016 #1
    • Thread moved from General Physics, thus no formatting template is shown.
    A mass-spring system is in free vibration after an initial excitation. There are no outside forces acting on the system. What is the value of the spring stiffness k (units of N/m; round your answer to a single decimal place)?

    Mass m = 0.6 kg
    Amplitude A = 0.4

    Using this equation:
    z(t) = A sin (w0 t)

    Where w0 = SQUARE ROOT k/m
    k is in the unit N/m and m is in the unit kg
     
  2. jcsd
  3. Sep 26, 2016 #2

    Hesch

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    Gold Member

    You must know ω0.

    The value of A doesn't matter.
     
  4. Sep 26, 2016 #3
    Okay, but I need help figuring out the value of ω0!
    I know the value of m (0.6 kg), so I just need to figure out k!
    Do you know how to figure that out?
     
  5. Sep 26, 2016 #4

    gneill

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    Staff: Mentor

    You cannot determine ωo or k from the given information. Is the question statement word-for-word complete?
     
  6. Sep 26, 2016 #5
    Yes, that's the entire question. There is also a graph if that helps at all.

    Screen Shot 2016-09-26 at 9.41.09 PM.png
     
  7. Sep 26, 2016 #6

    gneill

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    Staff: Mentor

    The graph is key to the problem. What information can you glean from the graph?
     
  8. Sep 26, 2016 #7
    Amplitude, frequency, and period.
    Is frequency equal to ω0?
    And frequency I believe would be 3, correct?
     
  9. Sep 26, 2016 #8

    gneill

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    Period T (Seconds) and frequency f (Hz) are both related to angular frequency ω (radians / sec). Do you know the relationships between these quantities? It comes up a lot so it's worth committing to memory.
     
  10. Sep 26, 2016 #9
    Angular frequency is equal to 2πf, if I remember correctly. So since f=3 in this example, would angular frequency be equal to 6π?
     
  11. Sep 26, 2016 #10

    gneill

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    Yes, but be sure to always include units when you quote values. In most cases in physics (and all sciences) a number alone is meaningless.

    So f = 3 Hz and ω = 6π rad/sec.
     
  12. Sep 26, 2016 #11
    Okay, that works out! Thank you so much for your help!!
     
  13. Sep 26, 2016 #12

    gneill

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    Staff: Mentor

    You're welcome. Good luck with your studies.
     
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