1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted