Transcript Advanced Precalculus Notes 7.5 continued Damped Motion

Advanced Precalculus Notes 7.5
continued Damped Motion
Friction and resistance remove the energy from
a moving system and cause the object to
decay to equilibrium. This is called Damping
the Motion.
Damping occurs in most physical systems. Sound
is damped in air, light is absorbed as it passes
through water, guitar strings don't vibrate
forever.
f ( x)  e x sin(12x)
bt

2m
d (t )  ae
2


b
2

cos  

t
2


4
m


A simple pendulum with a bob of mass 10 grams and a damping
factor of .8 gram/second is pulled 20 cm. from its at-rest position
and released. The period of the pendulum without the damping
effect is 4 seconds.
a) Find an equation for the position of the pendulum bob.
b) Graph the function.
c) What is the displacement of the bob at the start of the second
oscillation?
d) What happens to the displacement of the bob as time increases
without bound?
Graphing the Sum of Two Functions:
f(x) = x + sin x
X

2
0
3
2

2
x
sin x
x + sin x
Point on
graph
(
,
)
(
,
)
(
,
)
(
,
)
(
,
)
X

2
0
3
2

2
sin x
cos 2x
sinx +
cos 2x
Point on
graph
(
,
)
(
,
)
(
,
)
(
,
)
(
,
)
Assignment:
page 562:
3, 21, 22, 27, 33, 42