Physics

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A 1.2 kg block is attached to a horizontal 23 N/m spring and resting on a frictionless
horizontal surface. The block is set oscillating with amplitude 10 cm and phase constant –
π/2. A 2nd block with mass 0.8 kg moving at 1.7 m/s collides inelastically (the blocks stick
together) with the 1.2 kg block when it is at its maximum displacement. Determine the
frequency, amplitude, and phase constant (relative to the original t = 0) of the resulting
motion.

  • Physics -

    m2•v2 =(m1+m2) •v
    v= m2•v2/(m1+m2) = 0.8•1.7/(1.2+0.8) =0.68 m/s = v(max)
    ω =sqrt{k/(m1+m2)} = sqrt{23/2) = 3.4 rad/s.
    v(max) = A1• ω,
    A1 = v(max)/ ω = 0.68/3.4 =0.2 m.
    ω = 2•π•f,
    f = ω/ 2•π = 3.4/2•3.14 =0.54 Hz.

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