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Simple Harmonic Motion: Position, Velocity, & Acceleration

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    A 1.00-kg glider attached to a spring with a force constant 49.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -3.50 cm (that is, the spring is compressed by 3.50 cm).

    Find the position, velocity, and acceleration as functions of time. (Where position is in m, velocity is in m/s, acceleration is in m/s2, and t is in s. Use the following as necessary: t.)


    2. Relevant equations
    x(t)=Acos(ωt+∅)

    3. The attempt at a solution
    I know that the amplitude is going to be positive 0.035m
    Thus, x(t)=0.035cos(ωt+∅)

    Also, ω=√(k/m)=√(49/1)=7rad/s
    ∴ x(t)=0.035cos(7t+∅)

    The only thing I am still confused about is how to find ∅...Can anyone help please and thank you?
     
  2. jcsd
  3. Apr 22, 2012 #2
    Compare with simple Cosine graph y=Cos(θ).
    Check what is new function be if it is shifted to the left by certain radian.
     
  4. Apr 22, 2012 #3
    The phase shift for the cosθ would be ∏
    ∴ x(t)=0.035cos(7t+∏)

    Thank you!

    SOLVED.
     
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