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Finding phase constant in SHM

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data

    A block of unknown mass is attached to a spring with a spring constant 9.00 N/m and
    undergoes simple harmonic motion, along the x axis, with an amplitude of 10.0 cm. When the
    mass is halfway between its equilibrium position and its maximum positive displacement, its
    velocity is measured to be +30.0 cm/s. Calculate
    (a) the mass of the block,

    2. Relevant equations

    ??

    3. The attempt at a solution

    I tried using the x= A cos (ωt +∅) but i can't figure it out without time. HELP?? I know the answer is suposed to be m= 0.750kg but i don't understand how to get there.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 21, 2012 #2

    ehild

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    What is cos(ωt +∅) when the mass is halfway between its equilibrium position and its maximum positive displacement?

    What is the formula for velocity as function of t?
    How is ω related to mass?

    ehild
     
  4. May 24, 2012 #3
    Since OP not interested, i find the problem interesting since i just started on SHM.

    Using circular motion method.
    Since position is halfway between its equilibrium position and its maximum positive displacement,
    θ=60°
    VmaxCos(90-θ)=0.3 m/s
    Vmax=0.3x 2/√3

    F=mv2/r
    m=0.9 x 0.1 x 3/(0.36)
    m=0.75 kg
     
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