1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zinaida [17]
3 years ago
5

A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The

damping constant of the guitar string is 1.8, and the note produced has a frequency of 105 cycles per second.
a.) Write a trigonometric function that models the motion of the string.

b.) Using a graphing calculator, determine the amount of time t that it takes the string to be damped so that -0.24 y 0.24. Please be sure to show a screenshot of your graph.

Mathematics
1 answer:
liubo4ka [24]3 years ago
4 0

Answer:

The equation that represents the motion of the string is given by:

y =Ae^{-kt}\cos(2\pi ft)     .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

y =0.6e^{-1.8t}\cos(2\pi 105t)  

or

y =0.6e^{-1.8t}\cos(210\pi t)  

(a)

The trigonometric function that models the motion of the string is given by:

y =0.6e^{-1.8t}\cos(210\pi t)

(b)

Determine the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24

Using graphing calculator for the equation

y =0.6e^{-1.8x}\cos(210\pi x)

let x = t (time in sec)  

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that -0.24\leq y \leq0.24 is, 0.5 sec


You might be interested in
What is the area of a triangle with a base of 27 mm and a height of 10 mm?
nexus9112 [7]

Answer:

area of triangle = 135 mm²

Step-by-step explanation:

Area of a triangle = 1/2 × b × h

Area of a triangle = 1/2 × 27 × 10

Area of a triangle = 135 mm²

5 0
3 years ago
Read 2 more answers
Is 3/8 greater than 7/12​
Gennadij [26K]

Answer:no

Step-by-step explanation:put the two numbers in the same denominator

The least common denominator of 8 and 12 is 24. So to get 8 to 24 you multiply it by 3. So 3(3/8) is 9/24.

To get 12 to 24 you multiply it by 2. So 2(7/12) is 14/24. 9/24 is less than 14/24.

5 0
3 years ago
Your answer should be a polynomial in standard form (3b – 4)(b + 2)
Arlecino [84]

Answer:

The equation in standard form is: 3b^2 + 2b - 8.

7 0
3 years ago
Read 2 more answers
Plz help me on this!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
hram777 [196]

Answer:

1. 12y+20

2. 15c^{2}-18c

3. 18d-12

4. x=9

Step-by-step explanation

Hope this helps. I'm very sorry if I'm wrong

7 0
2 years ago
Read 2 more answers
Solve the following equations 3(x-2)= x+4
luda_lava [24]

Answer:

The answer is 9=9. Hope it helps :3

Step-by-step explanation:

3(5-2)=5+4

3(3)=5+4

9=5+4

9=9

5 0
3 years ago
Read 2 more answers
Other questions:
  • 3135 divided 5 and 1052 divided 4
    12·2 answers
  • Make k the subject for 3t = 7k/13 - 17 and 7k = 4k/3t - 11t
    13·1 answer
  • Which method do you prefer to use to find sums- count by tens and ones, use compatible numbers, or use friendly numbers and adju
    8·1 answer
  • AD _____ EC Choose the relationship symbol to make a true statement.
    5·2 answers
  • Solve for x.<br> 3(2x-3) +42-2=0
    6·1 answer
  • If the legs of an isosceles right triangle have a length of ft, the hypotenuse will have a length of?
    7·1 answer
  • Two containers designed to hold water are side by side, both in the shape of a
    14·2 answers
  • In the equation: y=3x, what is the 3 called?
    15·1 answer
  • Evaluate 5 · (x – 3) when x = 10.<br> 
    6·1 answer
  • Please help me!! I’ll give brainliest also!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!