Grade 11 math - HELP!

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Skyscrapers sway in high-wind conditions. in one case, at t=2s, the top floor swayed 30cm to the left (-30cm), and at t=12, the top floor swayed 30 cm to the right (+30cm) of its starting position.

a) what is the equation of a sinusoidal function that describes the motion of the building in terms of time?

b) if a damper is added to this building, it will reduce the sway (not the period) by 70%. what is the equation of the new function that describes the motion of the building in terms of time?

  • Grade 11 math - HELP! -

    I assume that the building goes directly from one extreme to the other in 12-2=10 seconds. Therefore the half-period is 10 seconds, or the period T=20 s.

    The neutral position is at (2+10)/2=6 seconds, when the displacement is zero.

    Thus we have
    Xo=30 cm = 0.3m
    X(t)=Xo sin((t-6)*2π/T), or
    X(t)=0.3sin((t-6)π/10)

  • Grade 11 math - HELP! -

    a) |a|= 30 cm
    1/2 period = 10
    period = 20
    k= 360/ period
    = 360/20
    = 18
    p = 2
    a = -30 (as a reflected cosine)
    therefore, d(t)= -30 cos{18(t-2)}
    b) Reduce sway = reduce of amplitude
    |a|= 100% - 70%
    = 30%
    |a| = 30 (.3)
    = 9 cos{ 18(t-2)}

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