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

A diver descended 21.83 feet in 5.9 minutes. What was the diver's average change in eleration per minute?​

Answers

3.7 feet per minute

A carpet measures 7 meters 3 decimeters in length and 4 meters 2 decimeters in width. What is its area in square meters?

Answers

Answer:

C

Step-by-step explanation:

change decimetres into metres

length - 7.3m

Width - 4.2m

to find an area, do length times width

7.3 x 4.2 = 30.66 square metres

I hope this helped :)

Answer:

C. 30.66 square meters

Step-by-step explanation:

The equation for area is A = L × W

L = length

W = width

Because a demimeter is 1 tenth of a meter your new measurements are 7.3 and 4.2.

multiply the measurements to find the area of 30.66² meters

65 - 2x ≥ 150, whats the answer!!!

Answers

Answer:

x <= -42.5

Step-by-step explanation:

65 - 2x >= 150

-2x >= 150 - 65

-2x >= 85

2x <= -85

x <= -85/2

x <= -42.5

Use the Distributive Property to solve the equation.
2(x+5)=20
The solution of the equation is

Answers

Answer:

2x+10=20 so x=5

Step-by-step explanation:

How do you find the Remainder when a polynomial in x is divided by a binomial of the form x-r?​

Answers

Answer:

see explanation

Step-by-step explanation:

If a polynomial f(x) is divided by (x - r) then the remainder is f(r)

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Take 2 points

(10,50)(30,60)

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{60-50}{30-10}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{10}{20}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

PLS HELP
Identify the range and domain of the function y=ln(x6).

Answers

The domain is {x ∈ R : x ≠ 0} (where R is the set of all real numbers), since x⁶ is a non-negative number for all real numbers x.

The range is R or the interval (-∞, ∞).

Miko filled two tanks with water. The ratio of the amount of water in Tank A to Tank B is 3 : 2. The total amount of water in both tanks is 210 ℓ. How much water must Miko pour from Tank A into Tank B so that both tanks have the same amount of water?

Answers

Step-by-step explanation:

answer is in the above picture

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] = 14

Answers

Answer:

This Inequality has no solution making it false.

Step-by-step explanation:

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] = 14

5,069=322

False

Hope this helps :)

Answer:

Step-by-step explanation:

Work out the midpoint A of the line segment B, where A(3,10) and B(5.8).

Answers

Answer:

Midpoint of (3,10) & (5,8) is (4,9)

Round the answer to the nearest cent.
5 1/2% tax on $20 is $

Answers

Answer:

goodmorning b

Step-by-step explanation:


In Jamal's county, there are
60 farms that cover about 8,370 acres of land.
If the farms are all approximately the same
size, how many acres is each farm?

Answers

Answer:

139.5

Step-by-step explanation:

8370/60

=139.5 per farm

The number of acres is each farm is 139.5 acres

Given that, 60 farms that cover about 8,370 acres of land.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number acres is each farm = Total number of acres/Number of farms

= 8,370/60

= 139.5 acres

Therefore, the number of acres is each farm is 139.5 acres

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

A recipe calls for 15 cup of milk for every 28 cup of flour. If Kenny wants to double the recipe, how many cups of flour will he need?

Answers

Answer:

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

well if the recipe is 28 cups of flower, and he wants to double it, Then its 56, the milk is extrenuis info.

Can you please give me the domain and the rage of the graph below? And not in (-∞,∞) form please, thank you

Answers

Answer:

d:-3, -2, -1, 0, 1

r: all numbers that are 4 and below

Step-by-step explanation:

You have a jar of jolly ranchers that contains: 15 cherry, 10 blue raspberries, 6 green apples, and 4 grapes.
Without looking, what is the probability that you select a green apple jolly rancher, eat it, then select a cherry?
The probability that both events occur is
which is
%. Round percent to the nearest whole
number.
Done and Review
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Answers

Answer:

9 / 119 or 8%

Step-by-step explanation:

there are a total of 35 candies, of which 6 are green and 15 are cherry

P(Green) = 6/35

P(Cherry) = 15/35

P(Green,Cherry) = 6/35 · 15/34

= 9/119 or 7.6%

Question is on picture attached

Answers

Answer:

Both triangles are congruent.

so 30/36 = 5/6 = 0.83333333333...

35/x  should also be 0.83333333333.. so 35/0.83333333333.. is x

x = 42

WILL GIVE BRAINLIEST! Consider the graph at right and answer the following questions.

Answers

Answer:

a.)A and B are the intersection between the two curves. The x coordinate is the equation

[tex]f(x) = g(x)[/tex]

Let's solve it

[tex]\frac12 (x-2)^3 +1 = 2x^2-6x-3\\x^3-6x^2+12x-8+2=4x^2-12x-6\\x^3-10x^2+24x=0\\x(x^2-10x+24)=0\\x(x-4)(x-6)=0[/tex]

We can see that if we substitute x= 0 or x= 4 the equation is verified.

b. The equation has a third solution, x = 6, that is too far to the right to be visible in the graph.

c. the x coordinate of C is the solution of [tex]f(x)=0[/tex] or [tex]\frac 12 (x-2)^3 +1=0\\(x-2)^3 = -2\\(x-2) = -\sqrt[3]2[/tex]

At this point let's guesstimate the cubic root of 2 -let's say the cubic root of 2 is equal to 1plus an error e, and since we know how to calculate the cube of a binomial, let's build it.

[tex](1+e)^3 = 2 \rightarrow 1+3e+3e^2+e^3 = 2[/tex] Now, assuming the error is small enough, it's square and its cube gets even smaller. (if the error is 0.1, it's square becomes 0.01 and the cube 0.01), let's ignore them. [tex]1+3e=2 \rightarrow 3e=1 e= \frac13[/tex] So, going back to our equation, we can tell that the right hand side is [[tex]\mathbb{R}[/tex]]-(1+\frac13)[/tex] Not perfect, but good enough. Let's solve it now.

[tex]x-2= -1-\frac13 \rightarrow x=1-\frac13 = \frac23[/tex]

Which seems close enough from the photo.

c. Domain of both function are the whole Real set, since they're polynomials. Range of f(x) is again the whole real set, since it's an odd degree polynomial. g(x) is a parabula and its range is for y above the vertex y-coord, which is [tex]y>g(\frac32) = 2(\frac94)-6(\frac32)-3 = \frac92 -3(\frac62) -\frac62 = \frac92-4\frac62= -\frac{24-9}2 = -\frac{15}2[/tex]

what is the length of a short leg of a 30-60-90 triangle shown below?

Answers

Answer:

5

Step-by-step explanation:

since 30-60-90 triangles are special right triangles, we know that if the short leg=x, the long leg= xsqrt(3). so the short leg= 5 sqrt(3) /(sqrt(3) = 5

the blank will be nagitve

Answers

Answer:

What would happen if someone doesn't put a negative comment in the blank?

Step-by-step explanation:

Answer:

numerical value??

Step-by-step explanation:

Use the method of your choice to factor 8m^3−343 completely.

Answers

52m(-872)=92.28763m
The method would be the power of m with 92=92.28763

Here you go ☺️ I NEED HELP SO HELP PLS

Answers

Answer:

the information above is not suffi

Step-by-step explanation:

hope it helps if wrong sorry

Answer:

The median height for tree 1 is greater.

Step-by-step explanation:

The height of tree 1 is greater therefore I believe the median will also be greater. I hope this helps.

Last year the cost of a season ticket for a football club was £560.
This year the cost of a season ticket for the club has been increased to £600.
Write down the increase in the cost of a season ticket as a fraction of last year's cost.

Answers

Answer:

The cost increased by 1/14

Step-by-step explanation:

A certain blueprint shows two fences. Fence A is 1 1/5 yards long but is 1 4/5 inches long on the blueprint. What is the unit rate for inches per yard on this blueprint? If the fence B is 4 yards long, how long is fence B on the blueprint?

Answers

Answer:

Q1: 3/72

Q2: 6 inches

Step-by-step explanation:

What is the unit rate for inches per yard on this blueprint?

First convert 1 1/5 yards to inches, so that becomes 216/5 inches.

To keep things consistent, let's convert the 1 4/5 inches to an improper fraction: 9/5 inches.

The question asks for inches per yard, so we substitute in the values:

[tex]\frac{\frac{9}{5} }{\frac{216}{5} }[/tex]

and simplify: 3/72

If fence B is 4 yards long, how long is fence B on the blueprint?

Convert 4 yards to inches (to comply to the ratio above): 144 inches

The ratio is inches to yards, so substitute in the value:

[tex]\frac{3}{72} = \frac{x}{144}[/tex]

and solve: 6 inches

100 POINTS IF U GET THIS RIGHT!

Answers

Answer:

The y-intercept is 4.

Step-by-step explanation:

Our equation: y = mx + b

m = slope

b = y-intercept

=> Now, let's compare:

=> y = mx + b = y = -7x + 4

We can tell that b = 4

Hoped this helped.

[tex]y =-7x +4 \\\\\text{ The above equation is in a form of y=mx+b, where b is the y-intercept}\\\\\\\text{Hence the y-intercept of the given equation is}~ 4.[/tex]

find the area of the parallelogram with the given information:​

Answers

Answer:

There is a area of triangle and there is two trapezium so 8×17=136

What does the value 12 represent in the function

Answers

Answer: The number twelve carries religious, mythological and magical symbolism, generally representing perfection, entirety, or cosmic order in traditions since antiquity.

Step-by-step explanation: If you're not talking about this type of 12 correct me.

What is an equation in point-slope form of the line shown in the graph, using the point (1, 5)?

Answers

Answer:

The point-slope form is  

y

+

6

=

1

5

(

x

4

)

or  

y

+

5

=

1

5

(

x

9

)

, depending on which point you use. If you solve for  

y

to get the slope-intercept form, both equations will convert to  

y

=

1

5

x

34

5

Step-by-step explanation:

y-5=[whatever slope is](x-1)

Round 70.74 to 2 significant figures

Answers

The answer is 71 since you count from the tenth space. So the first significant figure would be 7 and the second significant figure would be 0. As we know that we round up one number of the previous number is 5 or bigger.

help with this question please?!ASAP

Answers

V = 1/3 pi r^2 • h
V = 1/3 (3.14) (4)^2 • 12
V = 200.96 mm^3

Answer:

209.22 mm

Step-by-step explanation:

Point C has a _____ abscissa and a _____ ordinate.



positive, negative
positive, positive
negative, positive
negative, negative

Answers

Answer:

i think its b but im not that sure

Step-by-step explanation:

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