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

PLS HELP ASAP ILL GIVE BRAINLKEST

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Answer:

Its the bottom one x>5

Step-by-step explanation:

Graph: y < 1/3x+1/2 can someone graph this on a actual graph for me

Answers

Answer:

here you go

Step-by-step explanation:

i have added y < 1/3x+1/2  --> this shows more of range so i also attached what  y = 1/3x+1/2 would look like

next time use this -

search up: desmos graphing calculator

help me too with this one PLEASE

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Answer:   -___-

Step-by-step explanation:

Question 1 Two autobody shops charge different rates for repairs. Bobby's Garage charges at a rate described by the equation 'R=250+22t". Sherie's Garage rate is described by the equation 'R=170+30t". In both cases, t' is the number of hours worked and R is the rate charged in dollars. How many hours must pass for the two shops to charge the same amount?​

Answers

Answer:

t=12.5 hours Image transcriptions Bobby's Garage R = 200 + 18t Sherie's Gar

Step-by-step explanation:

I'm not sure what the rest is but I hope that can give you some sort of clue as to what it is :)

" t=12.5 hours Image transcriptions Bobby's Garage R = 200 + 18t Sherie's Gar"

what is 15/2 into a mixed number

Answers

7 1/2.

2 goes into 15 7 times with one left over.

Are (1,1.5) and (12,4) solutions to the equation y=1/4x+5/4

Answers

Answer:

The first set is a solution, the second is not.

Step-by-step explanation:

Testing by filling in the numbers into the equation:

(1, 1.5): x=1, y=1.5

⇒ 1.5 =? [tex]\frac{1}{4}[/tex] · 1 + [tex]\frac{5}{4}[/tex]

⇒ 1.5 =? [tex]\frac{1}{4}[/tex] + [tex]\frac{5}{4}[/tex]

⇒ 1.5 =? [tex]\frac{6}{4}[/tex]

⇒ 1.5 =? 1.5  ⇒ Correct: is indeed solution to the equation

(12, 4): x=12, y=4

⇒ 4 =? [tex]\frac{1}{4}[/tex] · 12 + [tex]\frac{5}{4}[/tex]

⇒ 4 =? [tex]\frac{12}{4}[/tex]  + [tex]\frac{5}{4}[/tex]

⇒ 4 =? [tex]\frac{17}{4}[/tex] ⇒ Incorrect: this is not a solution for the equation

Zoila bought a rectangular rug. The rug is 8 feet long by 5 feet wide. What is the area of the rug?

Answers

72ft squared is the answer

Answer:

Zoila bought a rectangular rug. The rug is 8 feet long by 5 feet wide. What is the area of the rug?

Final Answer: The area of the rug is 1.6[tex]ft^{2}[/tex] .

Step-by-step explanation:

What is Ask? - What is the area of the rug?

Given - 8 feet long by 5 feet wide

Operation - Divide

Solution:

You can use Partial quotient or Algorithm or Box method dividing any number.

5 ÷ 8 = 1.3

But why 1.6?

Because it is the decimal form of it and it is an improper fraction.

[tex]\frac{8}{5}[/tex] OR 1.6 OR [tex]1\frac{3}{5}[/tex]

Final Answer: 1.6 [tex]ft^{2}[/tex] is the area of the rug.

Hope it helps

#LetStudy

Select the correct answer.

Answers

Answer:

C

Step-by-step explanation:

ΔFDC and ΔFBA are similar          AA Similarity

Graph this inequality:
y ≤ 1/4x

Answers

Graph this inequality:

Which is the best estimate?

Answers

7.5 bbbbbbbbbbbbbbbbbb

A line contains the point 4,5 slope of -2 what point is also on the line.

Answers

Answer:

Step-by-step explanation:

First solve the equation for the line: Use the Point Slope form of a line: (y−y1)=m(x−x1). (y−5)=23(x−(−4).

GHOST FACE CULT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! help me

Answers

Answer:

it would be A

Step-by-step explanation:

because 4x-7=1

x=2

4(2)-7=1

8-7=1

I hope this helps you

help me find a please

Answers

Answer:

Ok, so the total answer in going to be 180 degrees. You have that 180 degrees between the two angles divided by 5. Once you divide 180 by 5, you will get the answer that is A=36

Solve for u, z, y, or t.

Answers

Doubt --!!

Where is your question!??????

A company spent $2415 on a plane ticket for seven employees all the tickets cost the same amount how much did each ticket cost

Answers

Answer:

$345

Step-by-step explanation:

2415 divided by 7 equals your total per ticket.

if an angle is bisected to form two new 39° angles, what was the measure or the original angle

Answers

Answer:

78°

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

78°

Step-by-step explanation:

39 × 2 = 78

--

Bisected - Divided into two parts.

Question 10(Multiple Choice Worth 1 points)
(01.05 MC)
Which number line best shows the position of 13?
J3
ht
-4
-3
- 2
-1
0
1
3
2
4
13
-4
-3
- 2
.
-1
0
1
2.
3
4
13
+
1
-3
-2
-4
-1
0
2.
3
4
13
+
3
-4
-3
-1
0
1
2
4

Answers

Answer:

It's the first option

Step-by-step explanation:

√3 according to calculator is 1.73205...

And if you check the options given, you'd see that the first option is the closest answer

halfway between -23 and 23​

Answers

Answer:

0

Step-by-step explanation:

-23+23= 0

0 + 23 = 23

To meet the character limit.

Answer:

0

Step-by-step explanation:

first, you need to calculate the entire distance:

23 + 23 = 46

Now divide it by half:

46 / 2 = 23

And now substract & add this

-23 + 23 = 0

23 - 23 = 0

2(3х + 8) = 2х - 16 + 4х

Answers

Answer: 0= -32

Step-by-step explanation:

brainliest me

You deposit $5000 into a savings
account. If you cam a simple
interest rate of 3%, how much
interest will you earn after 5 years

Answers

$750
Because if you multiply 5000 by .03 that equals $150 which is the amount of interest per year then you can multiply that by 5 giving you $750

HELPPP PLEASEEEE………..

Answers

Answer:

the answer is 54°......

Quadratic Transformation Worksheet Nam Write the quadratic equation,
1. y = (x - 2)2 + 0 ​

Answers

M-ental

A-buse

T-o

H-umans

Subscribe to DreamfanBG for support.

Determine the solution for the following equation: (8x-8)3/2=64

Answers

x=6 1/3 because you must follow PEMDAS

Answer:

X=3

Step-by-step explanation:

Edge2021

When ordering pizzas, 5 pizzas cost $60. Does this mean 9 pizzas will cost $100? Write a proportion and use cross products.

Answers

Answer:

108$.

Step-by-step explanation:

two ferries start moving toward each other from opposite riverbanks, a and b. when they pass each other for the first time, the distance to riverbank b is 100 meters. each ferry starts its return trip as soon as it reaches its destination. when the ferries meet for the second time, the distance to riverbank A is 50 meters. what is the distance between riverbanks a and b? Help I will give 40 points

Answers

Let 'x' be the distance from THE far bank   where 700 is the distance to the NEAR bank

boat one has travelled 700    (rate = 700/unit time)         boat two has travelled   x    rate = x / unit time

boat one then travels   x  + 400  more      and boat two travels   700 + (700+x -400) more    when they meet

The time is the same      rate x time = distance      distance/rate = time     equate the distances divided by the respective rates

(700 + x + 400)/700     =    (  x  +  700     +  (700+x-400) )/x

1100x + x^2 = 1400x + 700000

x^2-300x -700000 = 0                         quadratic formula yields  x = 1000  

One boat travels 700   the other   1000 whe they first meet.....width of river =   700+ 1000 = 1700 m

anyone ?????????????

Answers

Answer:

g(4) = 8

g(6) = 12

Step-by-step explanation:

come on dude, easier than that?

A rectangular pool 12 meters by 8 meters is surrounded by a walkway of width x meters. At what
value of x will the area of the walkway equal the area of the pool?
Explain. (don’t send file)

Answers

X=3

x is the width of the sidewalk
The outside dimensions of the walkway are 12 + 2x by 8 + 2x
The total area is (12 + 2x)(8 + 2x)
The total area minus the area of the pool should be equal to the area of the pool

Hoped this helped!

Given the sequence 3, 1,-1, -3, ... use the arithmetic sequence formula to write an equation.
Then, find a32.

Answers

Answer:

a₃₂ = - 59

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = a₂ - a₁ = 1 - 3 = - 2 , then

[tex]a_{n}[/tex] = 3 - 2(n - 1) = 3 - 2n + 2 = - 2n + 5

Then

a₃₂ = - 2(32) + 5 = - 64 + 5 = - 59

309x29 WORK MUST BE SHOWN PLSSSS

Answers

Answer:

8961

Step-by-step explanation:

    3 0 9

×       2 9

____________________________

+   2 7 8 1

+   6 1 8  

____________________________

=  8 9 6 1

Solve for g.

7 − –3g = 13

g =

Answers

Answer: g=2

Step-by-step explanation:

Remove the parentheses

7- (-3)g=13

Move the constant to the right

7+3g=13

Calculate

3g=13-7

Divide both sides

39=6

Answer:

g=2

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