Answers
This is a simple harmonic motion exercise. The proof that the resultant force on the particle, at time t, is -225 Newtons is indicated below.
What is the proof that the resultant force on the particle, at time t, is -225x newtons?Note that we have been given the following:
Mass = 9kg,
Y = 45 N
ζ = 0.4 m
Then, Y/ζ = 45N/0.4m
= 112.5 N/m
Hence, the spring constant =
K = 112. 5N/m
From this point we can resolve the Amplitude (A):
Amplitude is given as:
A = CB - PB
= 0.6 - 0.5
A = 0.1m
I) So because one spring is elongated by x and the other is compressed by x, Hence, the spring force is:
F[tex]_{net}[/tex] = - Kₓ - Kₓ
= - 2Kₓ
= -2 x 112.5 x* X
F[tex]_{net}[/tex] = -225x Newton ..........Lets call this expression 1
From equation 1 above, we know that
Ma = -225x
a = (-225/m) x
⇒ a ∝ - x,
Hence, the motion is is simple harmonic in nature.
What is the period of the motion?
The time period, T = 2 π√m/K[tex]_{eq}[/tex]
Where, K[tex]_{eq}[/tex] = 2K
= 2π√(9/225)
= 2π * 3/15
= 2(22/7) * (3/15)
= 1.25714285714; thus
T ≈ 1.26 secs...............lets call this expression 2
What is the speed of the particle when it is 0.05 meters from C?Note that Angular Frequency is = 2π/T
= 2π/1.26
= 4.9866550057
ω = 4.99 rad/s
Since the velocity at any point x from the mean position is given by
V = ω √ (A² - x²); hence
V = 4.99 √[(0.1)² - (0.05)²
V = 4.99 x 0.0866
V = 0.432134
V ≈ 0.432..........Lets call this expression 3
What is the expression of x in terms of t?Along the x-axis, A simple harmonic motion can be depicted as:
x = A sin (ωt + Ф) ..........lets call this expression 4
where, Ф = Phase constant
At t = 0; x = A
A = A sinФ
⇒ SinФ = 1
⇒ Ф = π/2
Expression 4 becomes:
x = A sin (ωt + π/2)
Inserting the values of ω and A, we have
x = 0.1 sin (4.99t + π/2).........Lets call this expression 5a
or x = 0.1 cos (4.99t).......Lets call this expression 5b
Hence,
Sin(π/2 + Ф) = CosФ
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Related Questions
Read and answer each question: A hotel has 7 floors. The lobby, restaurant and gym are located on the ground floor. The guestrooms are on 1 stto 6 thfloors. 1. If there are 35 standard rooms on each floor, how many standard rooms are there? will mark as bralinst
Answers
There are 6 floor with guest rooms.
Multiply the number of floors by number of rooms per floor:
35 x 6 = 210 standard rooms.
Jonathon saves $4,000 at the end of each quarter for 10 years. Assume 12% compounded quarterly and find the present value.
A. $35,008.24
B. $92,459.08
C. $105,623.10
D. $88,459.08
Kaitlyn hopes to attend a college where tuition is $24,000 per year. She believes that tuition will increase at 4% for the 3 years until she plans to enter college. Find the quarterly payments needed to accumulate funds to pay the first year’s tuition if funds earn 8% compounded quarterly.
A. $1,597.20
B. $34.05
C. $2,012.87
D. $2,561.30
Answers
Answer:
Results are below.
Step-by-step explanation:
1. First, we need to calculate the Future Value:
FV= {A*[(1+i)^n-1]}/i
A= quarterly deposit
n= 10*4= 40
i= 0.12/4= 0.03
FV= {4,000*[(1.03^40) - 1]} / 0.03
FV= $301,605.04
Now, the present value:
PV= FV/(1+i)^N
PV= 301,605.04/(1.03^40)
PV= $92,459.09
2. First, we need to calculate the value of the first year of college:
FV= PV*(1+i)^n
FV= 24,000*(1.04^3)
FV= $26,996.74
Now, the quarterly payments:
FV= {A*[(1+i)^n-1]}/i
A= quarterly deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
i= 0.08/4= 0.02
n= 3*4= 12
A= (26,996.74*0.02) / [(1.02^12) - 1]
A= $2,012.87
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 50 POINTS !! DONT SKIP :((.
Answers
Answer:
Step-by-step explanation:
m= 25 and b= 450
y= 25x+450
I believe proportional
positive slope
please correct me if I am wrong
One face of a cube-shaped package has an area of 7 5/8 square inches what is the lateral surface area of the package in square inches
Answers
Answer:
232.57 square inches
Step-by-step explanation:
The computation of the lateral surface area of the package in square inches is shown below;
Let us assume the area of cube is a
Given that
a = [tex]7 \frac{5}{8}\ in^2[/tex]
As we know that in a cube there is a four faces so the lateral surface area would be
[tex]= 4a^2\\\\=4\times 7\frac{5}{8} ^2\\\\= 4\times (\frac{61}{8})^2\\\\= 4\times \frac{3721}{64} \\\\= 232.57[/tex]
= 232.57 square inches
bro please help me ill give brainliest to the first one to answer correctly. its for some iready assessment
Answers
Explanation : trust me bro
Answer:
The answer should be B
Step-by-step explanation:
Car A traveled farther at the same rate as Car B but A travelved more so the answer is B
Which of the following choices describes the sequence 12, 17, 22, 27, 32,…?
A. each term has two more than the previous term
B. each term has five more than the previous term
C. each term is twice the previous term
D. None of these choices are correct.
Answers
12+5=17
20-20+3847x1,00,000,000=?
Say #relatable if this is you
Answers
Answer: 384,700,000,000
Step-by-step explanation:
Answer:
20-20+3847x1,00,000,000 =
348699999982
Step-by-step explanation:
lol not me
A newsletter publisher believes that less than 25% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim
Answers
Answer:
There is enough evidence at the 0.05 significance level that the percentage is less than 25%.
Step-by-step explanation:
The question has no options. However, there are enough details to arrive at a conclusion.
Required
What can we conclude about the claim of the publisher.
From the question, we understand that the null hypothesis is rejected.
In statistics, a hypothesis is rejected, if the level of significance is less than the required or determined value.
In this case, the determined value 25% and the level of significance is 0.05
So, the conclusion on the claim is that there is enough evidence at the 0.05 significance level that the percentage is less than 25%.
A vendor has 10 balloons for sale: 5 are yellow, 2 are red, and 3 are green. A balloon is selected at random and sold. If the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow?
Answers
Answer:
4/9
Step-by-step explanation:
Answer:
4/9
Step-by-step explanation:
If sheeren had 7 friends and lost two how much would she have?
Answers
Answer:
sheeren would have 5 friends
Step-by-step explanation:
If you split the clock, which is a 360 degree circle into 10- minute intervals, what is the central angle of each interval?
Answers
Answer:
Since 15 mins are 90 degrees
10 mins are 60 degrees
which is the product of 15 5\12 A. 5 5\12 B. 6 1\4 C. 7 1\12 D. 7 3\4
Answers
Answer:
6 1/4
HOPE THIS HELPS!!!!!
PLS I WILL GIVE BRAINLIEST AND IT IS WORTH DOUBLE POINTS!!!
Sophia is paying for a meal which costs $35. She has a coupon for a 20% discount. After the discount, sales tax is added at a rate of 8%. How much does Sophia need to pay for this meal? Explain how you got your answer
Answers
Answer:
he has 0.56 cents
Step-by-step explanation:
Answer:
I think the answer is 30.24
take off that is because 35 - 20% equals$28 plus 8% tax equals 30.24 so that's how I got that
Solve the inequality 2n – 1 < 39
Answers
Answer:
n < 20
Step-by-step explanation:
2n – 1 < 39
Add 1 to each side
2n – 1+1 < 39+1
2n < 40
Divide each side by 2
2n/2 < 40/2
n < 20
Fionn observed that 91\%91%91, percent of the background checks he processes are for potential employees who have already interviewed. Let BBB be the number of background checks Fionn processes to get his first background check for a potential employee who has not yet interviewed for the job. Assume that the interview statuses are independent. Find the probability that the 8^{\text{th}}8 th 8, start superscript, start text, t, h, end text, end superscript background check that Fionn processes is the first for which the potential employee has not yet interviewed.
Answers
Answer:
0.05
Step-by-step explanation:
checked via khan academy
Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.
What is probability?
Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
We want to find that the first order placed by a new customer is the 5th.
We have that:
8% = 0.08 probability that an order is placed by a new customer.
1 - 0.08 = 0.92 = 92% probability that an order is placed by an old customer.
Probability that the first order placed by a new customer is the 5th:
First four all old, each with 0.92 probability.
Firth new, with 0.08 probability. So
[tex]p=(0.94)^4\times 0.08=0.0573[/tex]
Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.
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how many square yards of carpet are needed to completely cover a rectangular floor that measures 15 feet by 9 feet?
Answers
Answer:
0.6
Step-by-step explanation:
is (3,8) a solution to this system of eqautions?
y=7x+8
y=x+1
Yes or No?
Answers
Answer:
Step-by-step explanation:
plug the numbers in and see if it is true
x=3, y=8
y=7x+8
8=7(3)+8
8=29
is not true, so it is not a solution. even if it might be a solution for the other equation, it is not true for this equation so it is not a solution for this system
how to find an equation: since y=7x+8 and y=x+1, then
7x+8=y, and y=x+1
7x+8=y=y=x+1
7x+8=x+1
6x+8=1
6x=-7
x=-7/6
y=x+1
y=-1/6
solution: (-1 1/6, -1/6)
an anthill has a volume of 8792mm^3 of dirt. its radius is 20 mm. what is the height of the cone? explain how you found the height.
Answers
Answer:
Height, h = 20.99 millimeters.
Step-by-step explanation:
Given the following data;
Volume = 8792mm³
Radius = 20 mm
To find the height;
We know that the shape of an anthill is conical in nature.
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.r is the radius of the base of the cone.h is the height of the cone.Substituting into the equation, we have;
[tex] 8792 = \frac{1}{3} * 3.142*20^{2}*h [/tex]
[tex] 8792 = \frac{1}{3} * 3.142*400*h [/tex]
[tex] 8792 = \frac{1}{3} * 1256.8*h [/tex]
[tex] 8792 = 418.93*h [/tex]
[tex] Height, h = \frac {8792}{418.93}[/tex]
Height, h = 20.99mm.
Therefore, the height of the cone is 20.99 millimeters.
i need help with #4 please help
Answers
Answer:
12b-8+12b-8+9b +8=33b-8
PLS HELP ASAP GIVING 35 POINTS... If a rock has a mass of 1.5 - g / mL and displaces 5-mI. of water, what is the mass of the rock?
Answers
How can you tell how many solutions a linear equation will have by looking at the equation?
Answers
Answer:
A system of two equations can be classified as follows
Step-by-step explanation:
If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.
3x- 4x + x
Like terms or not Like terms?
Answers
Answer:
like terms
Step-by-step explanation:
they all are terms that include the letter x
Answer:
It should be Like Terms
Explanation:
Like terms are the terms which have the same variables with same exponent for each variable.
Example :
7x, 3x, - 4x
Unlike terms are the terms which have same variables or different variables.
If they have same variables, the exponents will not be same.
Example :
9x2, 5xy, - 4xy2, y, 6
A right triangle has leg lengths of 2.7 cm and 4.8 cm. What is the length of the hypotenuse? (Round to the nearest hundredth if necessary.)
Answers
Answer:
nñœñtîęñ do îñglęs...ææ
PLEASE ANSWER!! will mark brainliest
Answers
Answer:
it's the second one
Step-by-step explanation:
a^7/a^13
=1/a^6
=1/(a^2)^3
= 1/ 3√(a^2)^3
=1/(a^2)
(c^3)^3
=3√(c^3)^3
=(c^3)
hence as these results matches so I think option b is correct.
Can someone help me with this?
Answers
Answer:
ᴀ.)
Step-by-step explanation:
Hope you get it right!! :)
The number of points scored by the girls basketball team in their last ten games are listed below. Which measure of center best describes the data? 38, 42, 45, 39, 48, 46, 39, 42, 45, 72
Answers
Answer:
median i think
Step-by-step explanation:
Read the picture carefully...there can be more than ONE ANSWER
Answers
Answer:
D
Step-by-step explanation:
what is 6% of $4100.
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Answer:
$246
Step-by-step explanation:
Instant brainliest please help.
Answers
Answer:the second one
Step-by-step explanation:
Work out the area of the shaded shape.
3cm
3cm
11cm
4cm
The diagram is not drawn to scale.
Answers
Answer:
I don't exactly know so just use a calculator.
Step-by-step explanation:
I think you multiply it all to get the answer.