Identifying Damped Trigonometric Functions

Section 4.6

1. What exactly is a damped trig function?

2. Can you do 65 in step by step fashion?

 

Identifying Damped Trigonometric Functions

65.

f(x)=|x*cos(x)|



The amplitude of the function is decreasing as x approaches 0 from both directions.

damping factor: y=x

-x<=|x*cos(x)| <= x

 

Let me see if I get what you are saying.

The peak of the function is decreasing as x tends to the line x = 0 aka the y-axis. Yes?

The damping factor is the equation(s) that squeezes the original function amplitude, which in this case happens to be the lines y = x and y = -x. Yes?

 

yes

 

Very good.

 

Can f(x)=|x*cos(x)| be expressed as
f(x) = |x|•|cos x|? If so, then f(x) = |x| is the same as f(x) = x, which is y = x, the damping function.

Yes?

 

yes, |x*cos(x)|=|x|*|cos(x)|

 

How did you conclude the damping function is y = x?
Let me see.

y = |x| and y = -|x| form a giant X on the xy-plane.

Yes?

 

Question 66

f(x) = x • sin x

Matches with (a).

The amplitude of the function is increasing as x approaches 0 from both directions.

The damping factor is the line y = x.

You say?




Question 68

g(x) = |x| cos x

Matches with (c).

The amplitude of the function is increasing as x approaches 0 from both directions.

The damping factor is y = |x|.

You say?

 

correct

 

Yes. Very good. Tough section for sure.