Posted by **Christa** on Sunday, July 25, 2010 at 9:38pm.

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 -
**Henry**, Monday, July 26, 2010 at 1:22pm
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 -
**Henry**, Monday, July 26, 2010 at 1:44pm
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 -
**Henry**, Monday, July 26, 2010 at 1:51pm
Christa, the data on the time line

should be shifted one space to the right.

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