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3 June, 12:07

The position function x (6.0 m) cos[ (3p rad/s) t p/3 rad]gives the simple harmonic motionof a body. at t 2.0 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? also, what are the (e) frequency and (f) period of the motion?

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  1. 3 June, 14:38
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    The correct formula for this simple harmonic motion is:

    x = (6.0) cos [ (3 pi) t + pi/3 ]

    A. Calculating for displacement x at t = 2:

    x = 6.0 cos (19/3 pi)

    x = 6 (0.5)

    x = 3 m

    B. Velocity is equivalent to the 1st derivative of the equation. v = dx / dt

    Velocity v = dx/dt = - 18 pi sin (3pi t + pi/3)

    v = - 18 pi sin (6pi + pi/3)

    v = 49.0 m/s

    C. Acceleration is the 2nd derivative or the 1st derivative of velocity dv / dt

    Acceleration a = dv/dt = - 54 pi^2 cos (3pi t + pi/3)

    a = - 54 pi^2 cos (3pi * 2 + pi/3)

    a = 386.34 m/s^2

    D. Phase = pi/3

    E. frequency f = 3pi/2pi = 1.5Hz

    F. period = 1/f = 1/1.5 =.6667sec
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