i need help i couldnt figure this out...

A block of mass m = 3 kg is attached to a spring (k = 35 N/m) by a rope that hangs over a pulley of mass M = 6 kg and radius R = 6 cm, as shown in the figure. Treating the pulley as a solid homogeneous disk, neglecting friction at the axle of the pulley, and assuming the system starts from rest with the spring at its natural length, answer the following.

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  1. Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

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    Writeacher
  2. the following what? My gut feel is that you will be dealing with energy, and force in this.

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    bobpursley
  3. Block
    T is tension between block and pulley)
    F = m a
    m g - T = m a
    T = m(g-a)

    T - spring force = Torque/R
    T - k x = Torque/R
    Torque = I alpha (I is in moment of inertia table for M and R)
    T -k x = I alpha/R
    a = alpha R
    T - k x = I a/R^2
    m(g-a) - kx = (I/R^2)a
    m g = k x + ma +(I^2/R) a
    m g = k x +(m+I^2/R^2)d^2x/dt^2
    (This is a spring mass system with equilibrium at x = mg/k and 2 pi f=sqrt(k/(m+I^2/R^2)
    but onward
    split x into Xo + A sinwt
    then mg = kXo for steady result
    then
    x(t) time function = A sin wt
    then
    a = d^2x/dt^2 = -Aw^2 sin wt = -w^2 x
    0 = k x(t) - (m+I^2/R^2)w^2 x(t)
    w^2 = k/(m+I^2/R^2)
    like we could already see
    so we have a vibration at frequency w/2pi about the point mg/k

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