100 Points!!!
y(t) = distance of weight from equilibrium position

ω= angular frequency (measured in radians per second)

A = amplitude

Ø= phase (depends on initial conditions)

c1 = A sin

c2 = A cos


Prove that: Asin(ωt+Ø)=c2sinωt+c1cosωt


Note: c1 and c2 are actually with the number slightly below the letter, if that makes sense. It wouldn't let me type it that way. Anyway, if anyone can help I would really appreciate it! Thank you!

Answers

Answer 1

Answer:

An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as

x(t) = x0 + A cos(ωt + φ).

The object oscillates about the equilibrium position x0.  If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by

x(t) = A cos(ωt + φ).

A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.  Simple harmonic motion is repetitive.  The period T is the time it takes the object to complete one oscillation and return to the starting position.  The angular frequency ω is given by ω = 2π/T.  The angular frequency is measured in radians per second.  The inverse of the period is the frequency f = 1/T.  The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time.  It is measured in units of Hertz, (1 Hz = 1/s).

The velocity of the object as a function of time is given by

v(t) = dx(t)/dt = -ω A sin(ωt + φ),

and the acceleration is given by

a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.


Related Questions

Will give crown! Help

Answers

Answer: The slope is -5/7

Step-by-step explanation:

Slope is rise/run

The rise is -5, and the run is 7

This is why the slope is -5/7

Answer:

The rise is 6 and the run is 7 6/7

biggg factssss♡♡♡♡lm.aoo​

Answers

Answer:

this is soo deep lol. free point epic pogg

ASAP I AM BEING TIMED I WILL MARK BRAINLIST




In psychology, the word "Gestalt" refers to

 A. a personality type

B. an adaptation that increases chances of survival 

C. the organization of parts into a whole pattern

 D. a learned response to a stimulus  E. the unconscious forces that drive behavior

Answers

Answer:

C. the organization of parts into a whole pattern

Step-by-step explanation:

Amplitude of 16 units, a period of 5 units, a vertical displacement of 3 units up and a phase shift of 2.5 units left.

Answers

The question is incomplete. The complete question is :

A sine function that has an amplitude of 16 units, a period of 5 units,a vertical displacement of 3 units up and a phase shift of 2.5 units left. Graph this function and show each step.

Solution :

The standard form of the sine function is

y = a sin (bx - c) + d

Here given :

Amplitude, a = 16

Period :   [tex]$\frac{2 \pi}{|b|} = 5$[/tex]

            ⇒ [tex]$b = \frac{2\pi}{5}$[/tex]

Phase shift :  [tex]$\frac{c}{b} = 2.5$[/tex]

                   [tex]$\Rightarrow \frac{c}{2 \pi/5}=\frac{5}{2}$[/tex]

                  ∴ [tex]$c = - \pi$[/tex]

The vertical displacement : d = 3 units up

Now substituting a, b, c and d values in the standard form gives :

[tex]$y = 16 \sin \left( \frac{2 \pi}{5}x -(- \pi)\right) + 3$[/tex]

[tex]$y = 16 \sin \left( \frac{2 \pi}{5}x + \pi\right) + 3$[/tex]

The graph is attached below.

A family restaurant chain wants to test the market for a new menu item: a grilled chicken sandwich with chipotle salsa. They are interested in both how to market the item and the right price to charge for it. They decide to offer the sandwich at 60 different restaurants in the chain, using two different descriptions on the menu. Half the restaurants' menus will emphasize "healthy eating" and half will emphasize "value." These two groups of restaurants will be further divided in three groups, each charging either a High, Medium, or Low price for the sandwich. After a month, they will measure what proportion of customers order the new sandwich.

Answers

Answer:

Experimental units, factors & treatments in experiment.

Step-by-step explanation:

Experimental Units are the 60 restaurants.

Factors are the : Menu description & price

Treatments in experimental design : Healthy Low Price, Healthy Medium Price, Healthy High price & Value low price, Value medium price, Value high price.

Complete the statement
Isosceles triangle A ABC has congruent angles at B and C. If BC is bisected at D and AD is drawn, by the side, side, side triangle congruence postulate,
(1 point)
O AADB AADC
O AADBA AABC
Ο ΔΑΒCA ΔΑDC
O AADB ADCA

Answers

Answer:

∆ ADB = ∆ ADC

Find ln(-127.1).
this question must be at least 20 characters long so here’s some extra characters but that’s the whole question^

Answers

Answer:

The natural logarthim of a negative is undefined.

What is the equation of the line that passes through the point (4,−7) and has a slope of -1/2?

Answers

Step-by-step explanation:

y = -0.5x + c

When x = 4, y = -7.

=> (-7) = -0.5(4) + c, c = -5.

Therefore the equation is y = -0.5x - 5.

Answer:

y = -1/2 x - 5

Step-by-step explanation:

y = mx + b

m = slope = -1/2

y = -1/2 x + b

-7 = -1/2 * 4 + b

-7 = -2 + b

b = -5

y = -1/2 x - 5

easy multiple choice!

Answers

Answer:

-4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

4x + 5y = -12

-2x + 3y = -16

Step 2: Rewrite Systems

-2x + 3y = -16

Multiply everything by 2:                    -4x + 6y = -32

Step 3: Redefine Systems

4x + 5y = -12

-4x + 6y = -32

Step 4: Solve for y

Elimination

Combine 2 equations:                    11y = -44Divide 17 on both sides:                  y = -4

Answer:

-4

Step-by-step explanation:

Have a great day, my dudes!

What is the measure of AC?

Answers

Answer:

A or B

Step-by-step explanation:

Helpppppppppppppppppppppppp

Answers

Answer:

Step-by-step explanation:

nose maffddnojgjfkufieo3owoeoiff

Give an example of a data set with an outlier. Describe how the outlier affects the mean, median, and mode of the data ​

Answers

Answer:

Outlier An extreme value in a set of data which is much higher or lower than the other numbers. ... Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Step-by-step explanation:

Hope it is helpful....

Plz help I will give your brainliest

Answers

Table goes from
X,y
2, 6
4,12
6, 18
8, 24
12, 30
After you’re going to plot the graph on 2x and 6y so basically (2,6) hope this helps

Which number line shows the solution of 6x-12 > -6? A. -10 - - - -6 -5 4 2 -1 0 1 2 3 B. -10-9-8 -6 5. -2 -1 0 1 2 3 4 5 6 7 8 9 C. 69 -10-9-8 -6 -5 -4 الم re 4 5 6 7 8 9 10 D. -10-9-8 6 7 8 9 10​

Answers

Answer:d

Step-by-step explanation:

The number line that represents the inequality 6x - 12 > -6 is (D)

How to determine the number line?

The inequality is given as:

6x - 12 > -6

Add 12 to both sides

6x > 12 - 6

Evaluate the difference

6x > 6

Divide both sides by 6

x > 1

The number line that represents the above inequality is (D)

Read more about number lines at:

https://brainly.com/question/10851163

PLEASE PLEASE HELP 25 POINTS I WILL MARK BRAINLIEST

Answers

Answer:

D

Step-by-step explanation:

(3, 9) (-3, 5)

 0 is in the middle       7 is in the middle

for x: 3 2 1  0  -1 -2 -3   for y: 9 8  7  6 5

Thus, (0, 7) is the midpoint between (3, 9) and (-3, 5)

-4(2-5b)=132
whats b?

Answers

Answer:

b = 7

Step-by-step explanation:

- 4(2 - 5b) = 132

- 4 × 2 - 4 × (- 5b) = 132

-8 + 20b = 132

20b = 132 + 8

20b = 140

b = 140/20

b = 7

Thus, The value of b is 7

-TheUnknownScientist

A pickup truck carrying 10*3 identical bricks weighs 6,755 pounds. If the empty truck weighs 6,240 pounds, what is the weight of each brick? Explain how you solved the problem.

Answers

Answer:

The truck now weighs 2130 kilograms. Hope this helps.

Step-by-step explanation:

The height of a parallelogram is 5 feet more than its base. If the area of the parallelogram is 204 feet, find its base and height

Answers

Step-by-step explanation:

Let

base=x

height=x+5

we know that in a parrelogram

[tex]\boxed{\sf Area=base×height}[/tex]

Substitute the values

[tex]{:}\rightarrowtail\sf x(x+5)=204 [/tex]

[tex]{:}\rightarrowtail\sf x^2+5=204 [/tex]

[tex]{:}\rightarrowtail\sf x^2=204-5 [/tex]

[tex]{:}\rightarrowtail\sf x^2=199 [/tex]

[tex]{:}\rightarrowtail\sf x=\sqrt {199}[/tex]

[tex]{:}\rightarrowtail\sf x=14.1[/tex]

[tex]{:}\rightarrowtail\sf base=14.

1feet[/tex]

[tex]{:}\rightarrowtail\sf Height =14.1+5=19.1feet [/tex]

how many times does 35 go into 78?​

Answers

Answer:

It goes in 2 times

Step-by-step explanation:

Can i have branliest, so i can go up a rank?

Answer:

35 goes into 78 two whole times but, it goes into it 2.22857143 times, or rounded to 2.23 times. the answer you put down depends on the directions.

PLZ ANSWER.. I NEED HELP!?!?

factorise x^2+5x+6​

Answers

Answer:

there is no like terms

Step-by-step explanation:

Answer:

(x+2)(x+3)

Explanation:

(x+2)(x+3)

If you simplify this, you get:

x*x = x^2

x*3 = 3x

2*x = 2x

2*3 = 6

If we add these all together we will have:

x^2 + 3x + 3x + 6

Combine like terms

x^2 + 5x + 6

What are the zeros of fx) =-8x+ 16? Yes

Answers

Answer:

There is one Zero.

Step-by-step explanation:

Hope this helps:)

The zeros are 2 but I am not sure

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.

Answers

Answer:

if you fill them all in corectly you should get not A

Not C NOR D THE ANSWER IS B 10 plus 14 equals 24 and 3 times 10 equals 30 and plus 5 times 14 equals 70 so the answer is B

tep-by-step explanation:

the coffee pub has cans of coffee that weigh 3 1/4 pounds each. the pub has 8 1/2 cans of coffee left. what is the total weight of 8 1/2 cans ? show your work​

Answers

Final Answer: [tex]27\frac{5}{8}[/tex] pounds

Final Answer Reason: The total weight of [tex]8\frac{1}{2}[/tex] cans would be [tex]27\frac{5}{8}[/tex] pounds

Steps/Reasons/Explanation:

We'll need to find the total weight of [tex]8\frac{1}{2}[/tex] cans, so we would need to multiply [tex]3\frac{1}{4}[/tex] cans by [tex]8\frac{1}{2}[/tex] cans. We are solving for the total weight of [tex]8\frac{1}{2}[/tex] cans.

Question: The coffee pub has cans of coffee that weigh [tex]3\frac{1}{4}[/tex] pounds each. The pub has [tex]8\frac{1}{2}[/tex] cans of coffee left. What is the total weight of [tex]8\frac{1}{2}[/tex] cans?

Solve For: The total weight of [tex]8\frac{1}{2}[/tex] cans.

Steps: Multiply to find total weight of [tex]8\frac{1}{2}[/tex] cans.

[tex]3\frac{1}{4}[/tex] × [tex]8\frac{1}{2}[/tex]

= [tex]\frac{13}{4}[/tex] × [tex]\frac{17}{2}[/tex]

= [tex]\frac{221}{8}[/tex]

= [tex]27\frac{5}{8}[/tex]

~I hope I helped you :)~


I need help with this asap

Answers

it is c !!!!!!! :))))

your answer must be simplified
−3 < x -10

Answers

Answer:

[tex]x>7[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that,\\-3<(x-10)\\Now,\\By\ adding\ both\ the\ sides\ by\ 10,\\(-3)+10<(x-10)+10\\Hence,\\10-3<x-10+10\\7<x\\Or,\\x>7[/tex]

What are the next two terms in the sequence 22, 15, 8, __, __? 1, -7 2, -4 2, -6 1, -6

Answers

Step-by-step explanation:

The sequence is an AP with common difference -7.

Therefore the next 2 terms are 1 and -6.

The next two terms are ( 1, - 6 ) so the correct answer is option D.

What is arithmetic progression?

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The next two numbers will be calculated as:-

22, 15, 8, __, __

Common difference = 15 - 22 = -7

Add this common difference in 8 to find the next term.

Next term = 8 - 7 = 1

Again add -7 to 1 to find the next term.

Next term = 1 - 7 = -6

Therefore the next two terms are ( 1, - 6 ) so the correct answer is option D.

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ2


Which trigonometric identity can be used to prove the given statement?
tan0 cos0 = sin0

Answers

Answer:

Step-by-step explanation:

Free trigonometric identity calculator - verify trigonometric identities step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy.

The following temperatures were recorded in Pasadena for a week in April: 87, 85, 80, 78, 83, 86, 90. Determine the interquartile range. Type a numerical answer in the space provided.

Answers

Answer:

7

Step-by-step explanation:

87 - 80 = 7

Match the equation and the description non-proportional Realationship

Answers

Answer:

A. [tex]y =\frac{7}{8}x+1[/tex]

B. [tex]y = -10x[/tex]

C. [tex]y = 2.5x - 7[/tex]

D. [tex]y = 1.2x[/tex]

E. [tex]y = -5x -8[/tex]

Step-by-step explanation:

Let the descriptions be A to E.

First, we need to note the followings.

An equation is of the form

[tex]y = mx + b[/tex]

[tex]m = slope[/tex] and [tex]b = y\ intercept[/tex]

A. Non proportional graph with positive y intercept

From the list of options, only

The slope of [tex]y =\frac{7}{8}x+1[/tex] is positive

and y intercept is also positive

B. Negative slope and pass through the origin.

Negative slope means m is negative

From the list of options

[tex]y = -10x[/tex] and [tex]y = -5x -8[/tex]

Origin implies (0,0)

i.e: [tex]x = 0[/tex] and [tex]y = 0[/tex]

For y = -10x

[tex]0 = -10 * 0[/tex]

[tex]0 = 0[/tex] --- This is true

For [tex]y = -5x -8[/tex]

[tex]0 = -5 * 0 - 8[/tex]

[tex]0 = 0 - 8[/tex]

[tex]0 = -8[/tex] --- This is not true

Hence:

[tex]y = -10x[/tex] fits this description

C. Increases from left to right and b is negative

For b is negative, we have the following:

[tex]y = -5x -8[/tex] and

[tex]y = 2.5x - 7[/tex]

An increment from left to right, means the slope is positive.

So, we have:

[tex]y = 2.5x - 7[/tex]

D. Positive slope and contains (0,0)

From the options, we have the following functions left:

[tex]y = -5x -8[/tex] and

[tex]y = 1.2x[/tex]

But [tex]y = 1.2x[/tex] has a positive slope and also contain (0,0) because

[tex]0 = 1.2 * 0[/tex]

[tex]0 = 0[/tex]

E. Negative m and Negative b

[tex]y = -5x -8[/tex] has these descriptions

Write the equation of the table shown below.
Х
0
2
5
9
12
у
4
6
9
13
16

Answers

Answer:

sorry... but the image is all black

I cant see anything

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