MathPre Cal & Trig
posted by Christa on .
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).

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