Question

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).

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

d(t) = -10cospi/2(x-2)+10

Answer 5

a pendulum swings back and forth taking 2 seconds to move from the position directly above from point a to the position directly above point b, as shown in the figure below. the distance form a to b is 20 cm. let d be the horizontal distance from her pendulum to the (dashed) centre 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 centre line at time t = 0 and moving to the right.


a) assume that the motion of the pendulum can be described by a sinusoidal function. Sketch the graph of d versus t for 0<\ t <\ 8.

b) write a sine equation that describes your graph