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Math Help - Simple Harmonic Motion

  1. #1
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    Exclamation Simple Harmonic Motion

    A particle, moving in SHM has period 2T. It starts from rest. Show that it gets halfway to the centre after T/3 and attains half its maximum velocity in time T/6
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    Quote Originally Posted by UltraGirl View Post
    A particle, moving in SHM has period 2T. It starts from rest. Show that it gets halfway to the centre after T/3 and attains half its maximum velocity in time T/6
    Particle starts from rest. A = Ao at t = 0. Hence equation of SHM is
    A = Aocos(ωt)
    A = Ao/2
    Ao/2 = Ao*cos(ωt)
    1/2 = cos(ωt)
    π/3 = 2π*t/2Τ
    Hence t = T/3.
    Velocity v = - vo*sinωt.
    find t when v = vo/2.
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