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Math-Pre Cal & Trig

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A pendulum swings uniformly back and forth, taking 2 seconds to move from the position directly above point A to the position directly above point B.
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A . B
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(SIMPLE DRAWING)


The distance from A to B si 20 centimeters. Let d(t) be the horizontal distance from the pendulum to the center line at time t seconds (with distances to the right of the line measured by positive numbers and distances to the left by negative ones.) Assume that the pendulum is on the center line at time t= 0 and moving to the right. Assume that the motion of the pendulum is simple and harmonic. Find the rule of d(t).

  • Math-Pre Cal & Trig - ,

    velocity = 20cm / 2sec. = 10 cm /sec.

    A B
    d(cm) -10 -8 -6 -4 -2 0 2 4 6 8 10.
    t(sec) 1 .8 .6 .4 .2 0.2.4.6.8 1.

    The period of the oscillations or
    vibrations is the time required for
    the pendulum to go from A to B and
    back to A ( 40 cm ).
    T = 40 cm / 10cm/sec. - 4 sec. =
    Period
    f = 1 / T = 1 / 4 = .25 cycles per
    sec = 0.25 hertz.

  • Math-Pre Cal & Trig - ,

    A B
    d(cm)-10 -8 -6 -4 -2 0 2 4 6 8 10
    t(se) 1 .8 .6 .4 .2 0 .2 .4 .6.8 1

  • Math-Pre Cal & Trig - ,

    Christa, the data on the time line
    should be shifted one space to the right.

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