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

Which are shown on the diagram? Check all that apply.

Answers

Answer:

i think b,c,d and f

Step-by-step explanation:

we know 15% of 600 now what Is 100% of 600​

Answers

Answer:

100% of 600 is 600

Step-by-step explanation:

Answer:

600 is the correct answer

Step-by-step explanation:

thanks

What's the slope of (0,5) and (4,2)

Answers

2-5/4-0
-3/4

Slope is -3/4

Remember slope is y2-y1/x2-x1

y+1= 6/11(x+4) convert to standard form please WILL GIVE BRAINLIEST

Answers

your answer is:

6x - 11y = -13

~☆

Which is a qualitative graph?

Answers

Step-by-step explanation:

Qualitative graphs are graphs that are used to represent situations that do not necessarily have numerical values. Qualitative graphs represent the essential elements of a situation in a graphical form. For example, Graph A could represent a car that is accelerating at a constant rate.

The numerical information from the definitive quantified variables research is given and represented utilizing quantitative graphs.Qualitative drawings were graphics that are used for circumstances without any numeric value.In graphical form, quality graphs are indeed the primary components of the scenario.Each frequency of attributes and qualities of a data set instance should be known.This analysis allows the researcher or analysts to obtain more massive data sets with the integral feature.

Therefore, the "Second graph" is the qualitative graph.

Learn more:

brainly.com/question/17146063

For a given input value aaa, the function hhh outputs a value bbb to satisfy the following equation. 3a-5=-4b+13a−5=−4b+13, a, minus, 5, equals, minus, 4, b, plus, 1 Write a formula for h(a)h(a)h, left parenthesis, a, right parenthesis in terms of aaa. h(a)=

Answers

Answer:

3/2-3/4a

Step-by-step explanation:

just solve for b basically, also the 3/2 and 3/4 is a fraction so they're over eachother but it wont let me do that on here so yeah. also sorry this is very late so i dont know if im any help.

The required function h(a) is a = -4b +18

A simplified function h for a-5=-4b+13 to be determine.

What are functions?

A function is defined as for every input their is a certain output.Function is a type of relation, or rule, that maps one input to specific single output.

Here, we have a-5=-4b+13

a−5=−4b+13

a = -4b + 13+ 5

a = -4b +18

Thus, the required function h(a) is a = -4b +18

learn more about function here:

brainly.com/question/21145944

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(5, 4) (7,10)
find the slope

Answers

Answer:

3

Step-by-step explanation:

The difference between the y coordinates is 6.

The difference between the x coordinates is 2

The slope is rise over run so in this case, the rise is 6 and the run is 2.

This makes our slope:

6/2

This can be simplified to 3/1 so the slope is 3.

Explain how to graph 5 2 on the number line. A number line going from 0 to 3. There are 2 equals spaces between each number. The number line contains 0, point A is one-half, 1, point B is 1 and one-half, point C is between point B and 2, 2, point D is 2 and one-half, 3.

Answers

Answer:

point D

Step-by-step explanation:

To graph 5/2 on the number line is to find its mixed number.5/2 is a improper fraction and and is equal to 2 and 1/2.So 5/2 is on point D.Because there are 2 whole groups in 5 and 1/2 that makes the mixed number.

Good luck on your test or problem

Answer:

To graph 5/2 on the number line is to find its mixed number.5/2 is a improper fraction and and is equal to 2 and 1/2.So 5/2 is on point D.Because there are 2 whole groups in 5 and 1/2 that makes the mixed number.

Step-by-step explanation

the person above me was right

I need help on this please!!!!! It's for homework that's due today at midnight. Please show work.​

Answers

Answer:

Exact Form: 91/30, Decimal Form: 3.03 (repeating 3), Mixed Number Form: 3 1/30

Step-by-step explanation:

Convert the mixed numbers to improper fractions. Then, you find the LCD (Least Common Denominator) and combine/simplify.

The regular price of a CD player is $89. It is on sale at a 25% discount. What is the sale price of the CD player?

Answers

Answer:

$66.75

Step-by-step explanation:

You would multiply $89 by .25 to find out what 25% is, then subtract that from $89 to get $66.75

Answer:

$66.75

Step-by-step explanation:

Divide quadratics by linear expressions (with remainders)
Divide the polynomials.
Your answer should be in the form p(x) +
where p is a polynomial and k is an integer.
3
37
22 + 4
3
Stuck? Watch a video or use a hint.
Report a problem

Answers

Answer:

x + 3 + [tex]\frac{13}{x-3}[/tex]

Step-by-step explanation:

Divide using Synthetic division

dividing by ( x - 3)

Using 0 to represent the x- term

3 |  1  0   4

     ↓ 3    9

        +     +

   ------------------

     1   3    13 ← remainder

Thus

[tex]\frac{x^2+4}{x-3}[/tex] = x + 3 + [tex]\frac{13}{x-3}[/tex]

 

help me I need help on this

Answers

It’s 1 :) I hope it helps

Answer:

It is 1.

Step-by-step explanation:

Hope this helped have an amazing day!

15PTS PLEASE HELP ASAP!!
(dont write random answers pls!)

Answers

Answer:

to find the answer, you need to find the measure of the angle on the other side of the 142. and since it's a straight line, those two angles measures are =to 180 (they're supplementary angles). so the measure of that angle is 38 degrees. to find the measure of the remaining angle, you subtract the angle measures you already know from 180 (because the sum of interior angles in a triangle is 180.) to, the answer is:

180-90-38= 52 degrees or A

Solve for X

17
47
34
13

Answers

Answer:

So 180-94 =86 so then it becomes 60°, 86°, and 2x so you would then add 60 and 86 together and get 146 and 180 - 146 is 34 then divide by two and you get 17 so x=17°

Step-by-step explanation:

Sorry if that’s confusing

Answer:

x = 17

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

94° is an exterior angle of the triangle, thus

2x + 60 = 94 ( subtract 60 from both sides )

2x = 34 ( divide both sides by 2 )

x = 17

p l e a s e h e l p . taking test rnnn:))) thanksssss will mark brainliest

Answers

help with what you gave nothing to answer

Which of the following is a rational number?
A
B
V60
С
6
D
49

Answers

Answer:

b

can i have brainliest

Which function is equivalent to f(x) = -4(x + 7) – 6?

Answers

Answer:

f(x) = - 4x - 34

Step-by-step explanation:

Given

f(x) = - 4(x + 7) - 6 ← distribute parenthesis

     = - 4x - 28 - 6 ← collect like terms

     = - 4x - 34

In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample, students will calculate the proportion of blue marbles. Which of the following sample sizes will have the largest sampling variability?

5
10
15
20

Answers

Answer:

5

Step-by-step explanation:

largest variability

Plzzzzzzzz help I don’t understand

Answers

Answer:

Slope formula: y2-y1/x2-x1

Step-by-step explanation:

8-6/9-6= 2/0

Answer:

Step-by-step explanation:

Alright we need to prove that both the triangles are similar so lets get started

The slope formula is:

Slope = Change in y / Change in x

m = Δy / Δx

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\[/tex]

Where, m is the slope and [tex](x_1,y_1) , (x_2,y_2)\\[/tex] are any points on the line

In this graph we are given three points which are

(0 , 2) , ( 6 , 6) and (9 , 8)

So for our first triangle we use the 2 points (0 , 2) and (6 ,6) and calculate the slope,

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{6-2}{6-0}\\\\m=4/6\\\\m=2/3\\[/tex]

So the slope turns out to be 2/3 , Now for our second triangle use the 2 points (6 , 6) and (9 , 8)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{8-6}{9-6}\\\\m=2/3\\[/tex]

So we can see the the slope's are equal that's the answer to your first part.

Second part

Yes they are similar due to the property of corresponding angles where angle x of the first triangle equals angle x for the second triangle and angle y for the first triangle equals angle y for the second triangle and both the triangles have 90° se they are similar because all three angles are similar. (AAA = angle angle angle property) I have attached a to make you understand it better.

On the number line, what is the value of B?

— click on the picture for number line —

Answers

It’s -0.5




Can I have the brain thing
Answer: -.5

Plz give me brainiest

1. Karen had 15 Snicker Bars. She gave 7 to her brother. What percent did
she give away?

Answers

Answer:

46%

Step-by-step explanation:

Have a wonderful day/night!

Answer:

46.666666666667%

Step-by-step explanation:

Thats the percent she gave away

Pls help me with this :)

Answers

Answer:

looks like school work

Step-by-step explanation:

DO IT ON YOUR OWN

Tyler’s brother works in a shoe store.

a) Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was his commission?

b) The store bought a pair of shoes for $50, and sold it for $80. What percentage was the markup?

c) Tyler’s brother earns $12 per hour. The store offers him a raise—a 5% increase per hour. After the raise, how much will Tyler’s brother make per hour?​

Answers

Answer:

A)  $22.5

B) $12.6

C) ...

Sorry but i only know two! But i hope this helps you!

Answer:

a) 22.50

b) 12.60

c)  12.60

Step-by-step explanation:

men can do a work in 32 days in how many days will 24 men complete the same work​

Answers

Answer:

It will take 32/24, or 1 1/3 days, for 24 men to get the job done.

Step-by-step explanation:

Please help me fast ​

Answers

Answer:

5/4 do the 2 lines then add1 then u get the anwswr

Step-by-step explanation:

5/4 would be the answer.

Two airplanes are carrying food and medical supplies to a country in needOne airplane is carrying 63 meals and 51 medical The total the supplies on that airplane is The other airplane is carrying 77 meals and 51 medical kitsThe cost for the supplies on that airplane Write and solve a system of equations to find the price of one meal and the price of one third airplane is carrying 70 meals and 62 medical , what is the total cost of supplies

Answers

Answer:374

Step-by-step explanation:

you add them all then get the total

I CANT FIGURE THIS OUT!! WHATS 1+1! I WILL GIVE BRAINLIEST IF U KNOW THIS

Answers

OMG THIS IS SO DIFFICULT, BUT I THINK THE ANSWER IS 3

4 1/2 + 1 3/5 =
What is the sum in simplest form

Answers

Answer: 6 1/10

Step-by-step explanation: I don’t know the decimal form but I had this question so

Solve and describe the graph of the inequality: j + 16 ≥ -21

Answers

Answer:

j ≥ -37

Step-by-step explanation:

j + 16 ≥ -21

move constant to the right hand side and change its sign

j ≥ -21 - 16

calculate the difference (subtract)

j ≥ -37

The graph would be a closed circle on -37 with an arrow pointing to the right.

To solve and describe the graph.

What is inequality?

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions. The quality of being unequal or uneven.

Given that:

The inequality is

j + 16 ≥ -21

Move constant to the right hand side and change its sign

j ≥ -21 - 16

calculate the difference (subtract) the constant term

j ≥ -37

So, the graph would be a closed circle on -37 with an arrow pointing to the right.

Learn more about inequality here:

https://brainly.com/question/19846294

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How could the statement "12 less than x" be written?

Answers

Answer:

The statment would be written as "12 - x".

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