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.

)12sin()( xexf x

t

m

baetd m

bt

2

222

4cos)(

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 0

x

sin x

x + sin x

Point on graph

( , ) ( , ) ( , ) ( , ) ( , )

2

2

32

X 0

sin x

cos 2x

sinx + cos 2xPoint on graph

( , ) ( , ) ( , ) ( , ) ( , )

2

2

3 2

Assignment: page 562: 3, 21, 22, 27, 33, 42