A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 6 cm, find the modeling equation if it takes 4 seconds to complete one cycle. Be to show, illustrate and explain your work.

Answers

Answer 1

The motion of the mass as it moves on the bottom of the spring is a

repetitive motion.

[tex]\mathrm{The \ motion \ of \ the \ mass \ attached \ to \ the \ spring \ is \ }\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]

Reasons:

The general form of the equation of the simple harmonic motion of the

mass is d = a·sin(ω·t)

Where;

d = The distance of the mass from the rest position

a = The maximum displacement of the mass from the equilibrium position = 6 cm

ω = The frequency of rotation

t = The time of motion

ω = The frequency of rotation

[tex]\displaystyle \omega = \mathbf{\frac{2 \cdot \pi}{T}}[/tex]

Where;

T = The time to complete one cycle (the period of oscillation) = 4 seconds

[tex]\displaystyle \omega = \frac{2 \cdot \pi}{4} = \frac{\pi}{2}[/tex]

Combining the above values gives the modelling equation as follows;

[tex]\displaystyle d = 6 \cdot sin\left(\frac{\pi}{2} \cdot t \right)[/tex]

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Related Questions

1. Subtract the linear expressions.

(45x−5)−(13x+4)

What is the difference?

Enter your answer in the box. Enter fractions as simplified fractions.

2. Add the two expressions.

−2.4n−3 and −7.8n+2

Enter your answer in the box.

3. Subtract the linear expressions.

(−3.6x+9.4)−(1.9x+3.6)

What is the difference?

Enter your answer in the box.

4. Subtract 5x−2 ​​from​ −3x+4 .


A.2x + 2

B.8x−6

C.−8x+6

D.−8x+2
Please try and put the correct answers.
If all correct I will mark them brainilest

Answers

[tex](1)\\\\(45x -5) -(13x +4) = 45x-5-13x -4 = 32x -9\\\\\\(2)\\\\-2(4n) -3 + (-7)(8n) +2 = -8n-56n -1 = -64n -1 = -(64n+1)\\\\(3)\\\\(-3.6x+9.4) - (1.9x +3.6) = -3.6x +9.4 -1.9x -3.6 =-5.5x+5.8\\\\\\(4)\\\\-3x+4-(5x-2) = -3x+4-5x +2=-8x +6[/tex]

or
Find the slope of the line
y
=
9
5
x

9
5
.

Answers

Answer:

Step-by-step explanation: 56776

A rental car agency charges $220.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $380.00?

Answers

40 miles per week

Step-by-step explanation:

380-220 = 160÷4 = 40

You can travel 320 miles in one week for $320 miles.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A rental car agency charges $220.00 per week plus $0.25 per mile to rent a car.

If the amount is $380.

Then, 380 - 220 = 160

And 160 divided by 0.5,

= 160/0.5

= 320 miles.

Therefore, the required distance is 320 miles.

To learn more about the division;

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#SPJ2

If two line are perpendicular which statement is true

Answers

The two lines intersect each other to make it perpendicular
Hope this helps you. Have a great day

50 POINTS! The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?

Answers

The common difference d is

(41–11) / (10–5) = 6.

The first term is

11 - 6(5–1) = -13.

so , the first term is -13

Answer:

-13

Step-by-step explanation:

The fifth term:

[tex]a_5=a+4d = 11[/tex]

The 10th term:

[tex]a_{10}=a+9d=41[/tex]

Subtract side-by-side and find d:

9d - 4d = 41 - 115d = 30d = 6

Find the first term:

a = 11 - 4*6 a = 11 - 24a = - 13

can someone lease tell me the answer to this question i'm abt to ask? what is 1 + 1/4?

Answers

Answer:

1 1/4 or 5/4 or 1.25

Step-by-step explanation:

(i) Find i in terms of P and A.

(ii) If 2500 is invested 3 years ago has a present value of 2650, find the rate of interest, i (correct to one decimal place)

Answers

Answer:

See below

Step-by-step explanation:

Given formula:

[tex]A=P(1+i/100)^3[/tex]

(i)

Solve for i:

[tex]A/P=(1+i/100)^3[/tex][tex]\sqrt[3]{A/P}=1+i/100[/tex][tex]\sqrt[3]{A/P} -1=i/100[/tex][tex]i=100(\sqrt[3]{A/P} -1)[/tex]

(ii)

P = 2500, A = 2650, find i:

[tex]i =100(\sqrt[3]{2650/2500} -1)[/tex]i ≈ 2.0%

can you please help me

Answers

Answer:

i think it's the 6th option

Step-by-step explanation:

Which of the following fractions is less than 1
options: a) 1 1by4 b) 3/4 c) 5/4 d) 2 3by4

Answers

Answer:

B

Step-by-step explanation:

11/4=2.75

3/4=0.75

5/4=1.25

23/4=5.75

Answer:

3/4

Step-by-step explanation:

Proper fractions are less than 1

3/4 is proper fraction.(Numerator less than denominator)

[tex]\dfrac{5}{4}=1\dfrac{1}{4}[/tex]

The diagram shows 5 triangles. All lengths are in centimetres. Which two triangles are congruent to each other

Answers

Answer:

It should be A & D

Step-by-step explanation:

These two are the only ones that have the exact same numbers on all three sides. They are congruent based on SSS.

HELP PLEASE!!!! FASTT

Answers

Answer:

Domain (-3,-2,-1,0,1,2)

Range (-2,0,1,2,3)

This is not a function

Step-by-step explanation:

Domain (-3,-2,-1,0,1,2)

Range (-2,0,1,2,3)

one x-value with two y-values, (-1, 2) and (-1, -2)

not a function

Plotting the graph should be easy

left side are x-values

right side are y-values

HURRY I NEED IT FOR 3rd GRADE MATH

Whats 73 + 82

Answers

Answer:

155

Step-by-step explanation:

Answer: 155

Step-by-step explanation:

73

+82

155

Harley downloads 8 games the total amount of available memory used for the games 57.2 gigabytes

Answers

Answer:

each game takes up 7.15 gigabytes (assuming each game takes up the same amount of storage.

Step-by-step explanation:

57.2 divided by 8 is 7.15

Factor (x^2-9) (x^2-16)

Answers

Answer:

( x - 3 )( x + 3 ) ( x - 4 )( x + 4)

Step-by-step explanation:

( x^2 - 9 ) ( x^2 - 16 )

( x - 3 )( x + 3 ) ( x - 4 )( x + 4)

Hopefully this helps!

Brainliest please?

[tex](x^2 -9)(x^2 -16)\\\\=(x^2 -3^2)(x^2 -4^2)\\\\=(x+3)(x-3)(x+4)(x-4)[/tex]

Teddy
1House A is twice as tall as House B. How tall is House B?
House
Height (ft)
A
24
B

Answers

How tall is house a? If a is 24 ft tall than B is 48 ft tall

Answer:

12

Step-by-step explanation:

House A is 24. So divide it by two to get 12. Which is house B

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 86%? 0. 14 0. 86 0. 93 0. 99.

Answers

The critical probability assuming a confidence level of 86% is;

Option B; 0.86

We are given the confidence level as 86%. This means that the probability of the mean of the normally distributed population being true is 86%.

This means that the critical probability is the value of z at 86% or 0.86

So when we find the value of z at that value, we will use it to get the margin of error.

Read more about critical probability of Confidence level at; https://brainly.com/question/16112320

GIVING BRAINLIEST
A submarine is traveling along the surface of the ocean when they spot a pod of dolphins ahead. To avoid the dolphins, the submarine will dive and travel through the ocean. If the submarine wants to be 1.1 nautical miles below the dolphins after traveling 2.5 nautical miles, what dive angle must the submarine make? Write only the number rounded to the nearest angle.

Answers

Answer:

26 degrees

Step-by-step explanation:

The attached image shows how I interpret this question, and I assume you're meant to use trigonometry to solve.

From the perspective of the angle, we have a relationship between the opposite side, the hypotenuse, and the angle. Because the 2 sides are the opposite and the hypotenuse, we need the sine function, and because the angle is the unknown, we need the inverse sine function.

(soh cah toa)

[tex]sin(x)=\frac{opposite}{hypotenuse}\\\\sin^{-1}(\frac{opposite}{hypotenuse})=x[/tex]

Now, just plug in the 2 known values and solve for the unknown:

[tex]sin^{-1}(\frac{1.1}{2.5})=x\\\\sin^{-1}(0.44)=x\\\\x=26.1039[/tex]

The angle is 26 degrees, and you can check that by doing it in reverse:

[tex]sin(26.1039)=\frac{1.1}{2.5}\\\\sin(26.1039)=0.44\\\\0.44=0.44[/tex]

Jasmine is reading a book. She has finished 23 of the book and has 56 pages left to read. How many pages has she read

Answers

Answer:

She would have 33 more pages left.

Step-by-step explanation:

You would want to subtract 23 from 56.

what is 0.3% of 200

Answers

It’s 60 because you multiple .3 by 200

help plssah
answer the question...

Answers

Answer:

2

Step-by-step explanation:

12 people sharing an 8 gummy worm pieces how much per person will get equally show two ways

Answers

Divide it into 12 parts or into 66 2/3

What is an equation of the line that passes through the points (-4, 2) and (-8, -3)

Answers

Answer:

a line through (-4,2) and (-8,-3) has slope = (2+3)/(-4+8) = 5/4 = (y-2)/(x+4)

cross multiply

5x +20 = 4y-8

5x -4y =-28

Step-by-step explanation:

Troy studies porcupines and wants to estimate the population in a certain region. Troy catches 36 porcupines, marks them, and releases them. Then later, Troy catches 450 porcupines and observes that 18 of them are marked. To the nearest whole number, what is the best estimate for the porcupine population?

Answers

A Group of scientists caught and tagged  porcupines=140 A week later the scientists counted the porcupines=180

You have 2\3 of a pizza left from yesterday. You divide it into 4 equal pieces. What fraction of the pizza is each piece?​

Answers

Step-by-step explanation:

that means we divide 2/3 by 4.

2/3 / 4 = 2/3 / 4/1 = 2/3 × 1/4 = 2/12 = 1/6

so each quarter of the remaining 2/3 pizza is actually 1/6 of the complete pizza.

Which function represents a translation of the graph of v=x^2
by 10 units to the left?
O A. v=x^2+10
O B. v=(x+10)^2
O C. y=10x^2
O D, y=(x-10)^2

Answers

Answer:

B.

Step-by-step explanation:

That would be y = (x +10)^2.

What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.

Answers

Answer:

slope= 1/4

Step-by-step explanation:

8-5 over 8-(-4)= 3/12=0.25 = 1/4

I/4 8-5 over 8-(-4) = 3/12 = 0.25 = 1/4

expand and simplify (x-2)(x-3), please help

Answers

Answer:

hope it helps you

(•‿•).........

Which of the following transformation sequences will produce similar, but not congruent, figures?

Answers

Answer:

The selected choice (#2) is correct

Step-by-step explanation:

Any rigid transformation (moving a figure, rotating it, flipping it around will leave the transformed figure congruent with the original. Scaling it (=dilating it) will generate a new figure what is similar to the original: angles remains the same but sides are in proportion.

simplify √5(8+3√6)
I cant figure this problem out can someone help me?

Answers

The answer is correct

PLEASR HELP MEEEE ASAP​

Answers

Answer:

A: Yes, I agree. Why? Because if you look at the shape, its a triangle right, and a triangle both sides are equal, while the bottom line is not. But because both sides are equal, and half of the triangle is MPN and the other side is QPN, they both are congruent (or equal to)

B: Like I said, both MPN and QPN are both equal, and if you remove the P, it would still be the same because the shape has not changed.

I hope I helped :)

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