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15 October, 10:22

A strong gust of wind strikes a tall building, causing it to sway back and forth in damped harmonic motion. The frequency

of the oscillation is 0.5 cycle per second, and the damping constant is c = 0.9. Find an equation of the form

y = ke ctsin (wt)

that describes the motion of the building. (Assume that k = 1, and take t=0 to be the instant when the gust of wind

strikes the building. Assume y begins increasing at t = 0.)

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Answers (1)
  1. 15 October, 10:45
    0
    y (t) = e^ (-0.9t) sin πt

    Step-by-step explanation:

    We are given;

    Frequency; f = 0.5 cycles/s

    Damping constant; c = 0.9

    K = 1

    Now relationship between frequency and angular velocity is;

    f = ω / (2π)

    So, 0.5 = ω / (2π)

    ω = 0.5 x 2π

    ω = π

    So, we want to use the expression;

    y (t) = ke^ (-ct) sin ωt

    Plugging in the relevant values, we have;

    y (t) = 1•e^ (-0.9t) sin πt

    y (t) = e^ (-0.9t) sin πt
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