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Maximum velocity of a mass undergoing SHM

  1. Apr 27, 2014 #1
    Question; A 1 g mass is suspended by a spring and executes simple harmonic motion when released. At time t=0 the displacement is 40 cm and acceleration is -3.6 cm/s^2. What is the spring constant k? What is the maximum velocity of this mass? At what time would the modulus of the maximum velocity first be reached?

    My attempt:

    I done the first part of the question and found k to be 0.025 N/m

    Maximum velocity occurs when

    v = ωA, and at t=0 x=A?

    So hence maximum velocity would be 2 m/s

    Using ω^2= k/m

    Assuming the above is correct, maximum velocity would first be reached when the

    sin(ωt) term is first equal to zero?


    Any help would be great :) thanks
     
  2. jcsd
  3. Apr 27, 2014 #2
    You assumed that the displacement at time t=0 was the equilibrium displacement but given that there is an acceleration then this can't be the case.

    Imagine the spring hanging without the mass. Then y'=0.

    Next, hang the mass on the spring. Then y'= mg/k.

    Lastly, pull the mass down to y'=40cm and release at t=0.

    Set y = y' - mg/k and A = 40cm-mg/k.
     
    Last edited: Apr 27, 2014
  4. Apr 27, 2014 #3
    Ahh ok! I also realised I made an error in saying the cosine term would be equal zero, it would equal one at maximum velocity!! And thanks I will get on it right away
     
  5. Apr 27, 2014 #4
    Wouldn't the amplitude be

    A= y' + mg/k
     
  6. Apr 27, 2014 #5
    Ok I calculated A= 0.57 mm is this reasonable?
     
  7. Apr 27, 2014 #6
    I miss calculated,

    A= 39.6 cm
     
  8. Apr 27, 2014 #7
    This gives me a max velocity of

    1.96 m/s
    Which first occurs after 0.317 seconds
     
  9. Apr 27, 2014 #8
    OK, more reasonable.
     
  10. Apr 27, 2014 #9
    Sorry I posted rather to much there which post is that directed to?
     
  11. Apr 27, 2014 #10
    Post #7.
     
  12. Apr 27, 2014 #11
    Those values seem on then??
     
  13. Apr 27, 2014 #12
    Thanks a bunch for all your help
     
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