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Simple Harmonic Motion (SHM) question check

  1. Aug 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s.
    calculate;
    (I) the spring stiffness, k. (force per unit extension)
    (II) the maximum velocity of the sphere as it oscillates.
    (III) the maximum acceleration of the sphere as it oscillates.


    2. Relevant equations
    ω=2*∏/T

    3. The attempt at a solution
    my workings;
    (I) W=2*∏/T
    =2*∏/1.67
    W= 3.76rads-1

    w^2=m/k
    3.76^2=0.20/k
    k=0.20/3.76^2
    = 0.20/14.14
    k=1.41*10^-2 Nm-1

    (II) Vmax= +- W √A^2 - x^2
    but x=0 so
    Vmax= +- WA
    = +- 3.79 * 0.030
    Vmax= +- 1.13*10^-1 ms-1

    (III) amax= +- W^2 * x
    but x=A so
    amax= +- W^2 * A
    = +- 3.76^2 8 0.030
    amax= +- 4.24*10^-1 ms-2

    could you please check my answers for me, because, i don't know why, i just feel like I've gone wrong somewhere.
    thanks sarah x
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 24, 2012 #2

    Simon Bridge

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    Welcome to PF;

    (I) Reasoning looks OK.
    How did you calculate T=1.67(s?)
    In 12 seconds you get 20 cycles - how much time for one cycle?

    Usually better to combine equations before putting the numbers in - to avoid rounding errors.

    (II) and (III) OK reasoning ... you should keep the direction (+/-) since they ask for "velocity" rather than speed.
     
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