Identifying Damped Trigonometric Functions

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Section 4.6

1. What exactly is a damped trig function?

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


20211116_045746.jpg
 
Identifying Damped Trigonometric Functions

65.

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

upload_2021-11-17_14-9-5.png


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

damping factor: y=x

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

MSP42921fhc7g05a7a6eaa00005b9103d09793gc6c
 
Identifying Damped Trigonometric Functions

65.

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

View attachment 1068

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

damping factor: y=x

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

MSP42921fhc7g05a7a6eaa00005b9103d09793gc6c

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?
 
Identifying Damped Trigonometric Functions

65.

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

View attachment 1068

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

damping factor: y=x

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

MSP42921fhc7g05a7a6eaa00005b9103d09793gc6c


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?
 
Identifying Damped Trigonometric Functions

65.

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

View attachment 1068

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

damping factor: y=x

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

MSP42921fhc7g05a7a6eaa00005b9103d09793gc6c

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?


20211119_193606.jpg


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?

20211119_193711.jpg
 
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