The diffraction efficiency of a thin square-wave phase grating for the first diffraction orders can be calculated using the following expression:
η = (sin(Nδ/2)/Nsin(δ/2))^2
where η is the diffraction efficiency, N is the number of grating periods, and δ is the phase shift of the transmitted light.
In this case, the phase shift varies between 0 and ф radians, so we can write:
δ = ф/N
Plugging this into the previous equation, we get:
η = (sin(Nф/2)/Nsin(ф/2))^2
To find the value of ф that produces the maximum diffraction efficiency, we can take the derivative of η with respect to ф and set it equal to zero:
dη/dф = 0
After some algebraic manipulation, we get:
sin(Nф) = Nsin(ф)
This equation has multiple solutions, but the one that produces the maximum diffraction efficiency is given by:
ф = arcsin(1/N)
Substituting this value of ф back into the expression for η, we get:
ηmax = (sin(π/2N))^2
Therefore, the maximum diffraction efficiency of the grating occurs when the phase shift is equal to the arcsin of 1/N, and it is given by the square of the sine of half the period of the grating.
To find an expression for the diffraction efficiency of a thin square-wave phase grating with thickness varying with period A, and the phase of transmitted light jumping between 0 and ф radians, we can use the following formula:
Diffraction Efficiency (η) = (sin²(ф/2))/(ф/2)²
To find the value of ф that produces the maximum diffraction efficiency, we need to look for the maximum value of the function η. The maximum diffraction efficiency occurs when ф = π, which gives:
η_max = (sin²(π/2))/(π/2)² = 1
So, the maximum diffraction efficiency for the first diffraction orders of the grating is achieved when ф = π radians.
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What happens when a baseball player runs from home plate to 1st base, from 1st to 2nd base, from 2nd to 3rd; and then back to home plate?
an object is on a horizontal surface. three forces act horizontally on the object: 3 N to the left, 12 N to the right, 1 N to the left. At the same time, another three forces act vertically on the object: 4 N upwards, 10 N downwards , 2 N upwards.
determine the resultant horizontal and vertical forces acting on the object.
Answer:
Resultant horizontal force : 16 N
Resultant vertical force : 4 N
Explanation: Force acting on left : 3N
Force acting on left : 1 N
Forces acting on left : 3N + 1N = 4N
Force acting on right : 12 N
Resultant horizontal force : 12 N - 4 N = 16 N
Force acting upwards : 4 N
Force acting upwards : 2 N
Forces acting upwards : 4 N + 2 N = 6 N
Force acting downwards : 10 N
Resultant vertical force : 10 N - 6N = 4 N
You serve a ball with a mass of 3.8 kg. The ball leaves your hand with a speed
of 38 m/s. What is the ball's kinetic energy?
Answer:
Below
Explanation:
Kinetic Energy = 1/2 m v^2
K.E. = 1/2 ( 3.8 kg) ( 38 m/s)^2 = 2743.6 J
According to boyle's law, at a constant temperature, if the volume of a container of gas is decreased the pressure of the gas will __.
if the volume of a container of gas is decreased the pressure of the gas will increases.
Explain boyle's law.The pressure (p) of a given quantity of gas changes inversely with its volume (v) at constant temperature, according to this empirical connection, which was established by the physicist Robert Boyle in 1662. In equation form, this means that pv = k, a constant. The French physicist Edme Mariotte also found the connection (1676).
According to question:We know that
pv = k
v ∝ 1/p
So, if the volume of a container of gas is decreased the pressure of the gas will increases.
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If you change the 2 in front of 2O2 to a 3, what will be the change in the results on the right side of the equation?
A.) There are now 3CO2 molecules
B.) Nothing changes in the equation
C.) There is an extra O2 molecule left over
D.) There are now 3H2O molecules
The number of atoms on either side of the reaction equation must match for there to be a balanced reaction equation.
The correct option is C.
What called molecules?Whether it originate from the same element or another, two or more chemically bonded atoms make up a molecule. For instance, the combination of two atoms of hydrogen and an oxygen atom yields one mole of a material.
Do molecules have the name mole?Among the first things you discover in chemistry is this: Because atoms and molecules are so little, numbering them by the trillions and trillions is as useless as counting them one by one because even a few milligrams of a substance contain so many atoms or molecules. Therefore, chemists employ a unit known as the mole.
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Frank pushes with a force of 620 N on a filing cabinet with a mass of 60 g. The cabinet doesn’t move.
What can be inferred?
When Frank exerts push with a force of 620 N over a filing cabinet with a mass of 60 g. The cabinet doesn’t move. it can be inferred that The static friction force of the floor and cabinet is greater than 620 N.
What is static friction?A type of force which holds an object at the state of rest is termed as static friction. we can define the static friction as The resistance person feel when he attempts to move a stationary object over a surface without actually causing any relative motion between his body and the surface they are moving the object across.To know more about static friction visit
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The complete question is :
Frank pushes with a force of 620 N on a filing cabinet with a mass of 60 g. The cabinet doesn't move.
What can be inferred?
A. There are no other forces acting on the filing cabinet.
B. The static friction force of the floor and cabinet is greater than 620 N.
C. The net force of the cabinet is greater than 620 N.
D. The friction force of the floor and cabinet is less than 620 N.
A boy i winging a toy on apiece of tring in a vertical circle. The toy ha ma 150g and the radiu of circle i 0. 8m. A) he wing the toy with a linear velocity 2m/. Will the top move in a circle? explain your anwer
If the boy swings the toy with a linear velocity of 2m/s, the toy will move in a circle. The force required to maintain the toy's motion IS 750g * m/s^2
The linear velocity of an object moving in a circle is related to its angular velocity (measured in radians per second) and the radius of the circle. The linear velocity is given by the equation: v = r * w, where v is the linear velocity, r is the radius of the circle, and w is the angular velocity.
In this case, the radius of the circle is 0.8m and the linear velocity is 2m/s. Therefore, the angular velocity of the toy can be calculated as: w = v/r = 2m/s / 0.8m = 2.5 rad/s.
The toy has a mass of 150g and it moves in a vertical circle with a radius of 0.8m and a linear velocity of 2m/s, so it will move in a circle. The force required to maintain this motion is the centripetal force, which is given by the equation F = m * a, where F is the force, m is the mass of the toy and a is the centripetal acceleration. The centripetal acceleration is given by the equation a = v^2/r, where v is the linear velocity and r is the radius of the circle.
So, the force required to maintain the toy's motion is F = m * a = 150g * (2m/s)^2 / 0.8m = 750g * m/s^2
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8 PM THANK YOU SO MUCH!
A
excretion, because Energy is being released alongside carbon dioxide and water. (on a personal side note it sounds like what happens to your cells/body when you exercise.)
Which type of force does a window washer want acting on him when trying to keep the same position?
A. Large
B. Small
C. Balanced
D. Unbalanced
Balanced force does a window washer want acting on him when trying to keep the same position.
What is force?
Force is an external influence that is capable of changing the motion of a body, either by a push or pull, or by causing a change in the shape or direction of the body. Force is a vector quantity, meaning it has both magnitude and direction. It can be a result of either physical contact, like pushing or pulling, or a non-contact force, such as gravity, magnetism, or electricity. Force is a fundamental concept in physics and its effects are studied in numerous fields, from mechanics to thermodynamics. Force can be used to move objects, cause objects to change shape, or cause objects to accelerate. It is a powerful tool for understanding physical phenomena.
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5. Find the mass of a book that has a weight of 4.7 newtons.
The mass of the book is 0.48 g
According to the Newton's second law of motion
Force(F)= Mass(m) × Acceleration(a)
Here, Force (F) = 4.7 Newton (N)
The acceleration due to gravity (g) = 9.8 m/s²
We have to find the mass of the book.
Putting the given values in the equation F=m×a
4.7 N = m × 9.8 m/s²
m = 0.48 g (approx.)
Hence, the mass of the book is 0.48 g
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A 8. 43-newton force was applied for an unknown displacement; however, it is known that 376 joules of work was done. What is the value of the mystery displacement?.
The value of the mystery displacement is 8.74 m. We can find it by dividing the force value with the work that was done to the object.
How to calculate the value of the mystery displacement?As per given data are work(W) = 376 J and Force(F) = 43 N, we can use a formula that contain correlation between work and force. The formula is W = F * Δx where Δx is displacement value. Hence, in order to find the value of displacement, the calculation will be:
W = F * Δx
376 = 43 * Δx
Δx = [tex]\frac{43}{376}[/tex]
Δx = 8.74 m
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A chain of metal links with total mass m = 5 kg is coiled up in a tight ball on a low-friction table. You pull on a link at one end of the chain with a constant force F = 64 N. Eventually the chain straightens out to its full length L = 0.8 m, and you keep pulling until you have pulled your end of the chain a total distance d = 3.2 m (diagram is not to scale). m ------- 1000000000000000 T> (a) Consider the point particle system: What is the speed of the chain at this instant? V = m/s (b) Consider the extended system: What is the change in energy of the chain? AE = joules (c) In straightening out, the links of the chain bang against each other, and their temperature rises. Assume that the process is so fast that there is insufficient time for significant thermal transfer of energy from the chain to the table, and ignore the small amount of energy radiated away as sound produced in the collisions among the links. Calculate the increase in thermal energy of the chain. AEthermal =
The speed of the chain at this instant is 8.47 m/s. The change in energy of the chain is 204.8J. The increase in thermal energy of the chain is 25.6J.
Acceleration(a) of Centre of mass = F/m = 64/5 = 12.8 m/s2
a) v2 = u2 + 2as,....(1)
It defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.v is final velocity of centre of mass,
u is the initial velocity of centre of mass,
s is the displacement of centre of mass
s = d - L/2 = 3.2 - 0.4 = 2.8m
using equation 1,
V = [tex]=\sqrt{2as} =\sqrt{2*12.8*2.8}=8.47 m/s.[/tex]
Therefore, the speed of the chain at this instant is 8.47 m/s.
2. Change in energy = Total Work Done = Force*Displacement of point on which force is applied = 64*3.2 = 204.8J
Therefore, the change in energy of the chain is 204.8J
3. Change in Thermal Energy = Change in Energy - Change in Kinetic Energy = 204.8 - 0.5*m*v2
Change in Thermal Energy = 204.8 - 0.5*5*8.47*8.47 = 25.6J
Therefore, the increase in thermal energy of the chain is 25.6J.
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9. 5 people each pull with 200 N each on an object. What is the net force on the object?
Answer:
1000 N
Explanation:
The net force is sum of all forces when considering in a one-dimensional motion. Since each people pull the object 200 N then that means 5 people together would pull 5 × 200 N = 1000 N.
Therefore, the net force is 1000 N
What allows negative feedback to control a system
Answer:
The system has parts that sense the amount of output, allows negative feedback to control a system
Explanation:
How much does it cost to power a refrigerator for 30 days if it is rated at 200 watts and the power company chargers $0.035 per kWh
The required cost to power the refigerator is $5.04.
What is electric power?Electric power is the rate at which electrical energy is transferred by an electric circuit.
To calculate the amount it takes to run the refrigerator, we use the formula below.
Formula:
A = 24NCP/1000..................... Equation 1Where:
A = Amount it takes to power the refrigerator for 30 daysN = Number of daysC = Power company chargeP = Electric Power of the refrigeratorFrom the question,
Given:
A = 24×30×0.035×200/100A = $5.04Hence, the cost is $5.04.
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Make up a situation that involves 3 forces. Write it out and show a force diagram showing all three
forces.
A car is driving on a level road and has a force of 1000 N acting on it to the right. The road has friction acting on the car with a force of 200 N to the left. The car's engine is providing a force of 800 N to the right.
Force Diagram:
[1000N] ____________
|
|
|
[800N] ____________|
|
|
|
[-200N] ___________|
Where the arrow pointing to the right represents the force acting to the right, and the arrow pointing to the left represents the force acting to the left.
The force of 1000 N is the force of the wind pushing the car to the right. The force of 200 N is the friction acting on the car from the road trying to slow it down. The force of 800 N is the force provided by the car's engine pushing the car to the right.
Express, in terms of x, the value, in cents. of x pounds of 40-cent cookies and (30-x) pounds of 50-cent cookies.
The value, in cents. of x pounds of 40-cent cookies and (30-x) pounds of 50-cent cookies are x(40) + (30-x)(50) = 40x + 1500 - 50x = 1500 - 10x
What is pound?The pound is a mass and weight measurement unit that is used in both the imperial and American customary systems. It is equal to 16 ounces or 0.45359237 kilograms. It is used in a variety of contexts, including engineering, commerce and finance, as well as everyday use. In the United Kingdom and other countries of the Commonwealth of Nations, it is the basis of their currency; one pound sterling is equal to 100 pence. The origin of the pound dates back to the Roman Empire, when it was known as the libra.
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According to the given statement 1500 -10x represents the equation in terms of x.
Is pound a mass or force?The term "pound" can also refer to a unit of mass in other situations. The pound is a unit of mass, and the international standard sign for it is lb. The weight of the mass unit (pound-mass) onto Earth's surface is about equivalent to the force unit in the "engineering" categories (middle column) (pound-force).
We are assigned the task of expressing an equation in terms of x using the provided information.
In this case, we must multiply the pounds by the number of cookies.
Where,
x=pounds × cent cookies
In light of the fact that for x pounds of 40 cent cookies.
And (30-x) pounds of 50 cent cookies
Let us form an equations in terms of x:
⇒40x+50(30−x)
⇒40x+1500−50x
⇒1500−10x
As a result, 1500 -10x represents the equation in terms of x.
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A newspaper article states that when turning a corner a driver must be careful to balance the centripetal and centrifugal forces to keep from skidding write a letter to the editor that describes physics errors in this article ?
can someone please explain centripetal and centrifugal forces, whats the difference and how would they effect friction if at all?
Centripetal force is the portion of a force exerted on an object in curvilinear motion that is directed at the axis of rotation or the centre of curvature. A fictitious force that moves in a circle and is directed away from the centre is called centrifugal force.
What is meant by Centripetal force?Any force that induces a shift in velocity direction toward the centre of a circular motion is referred to as a centripetal force.Centripetal force is caused by the part of the force that is perpendicular to the velocity. The tension in a tether ball's rope, the gravitational pull of Earth's gravity on the Moon, the friction between roller skates and a rink's floor, the force a car feels on a banked road, and the forces acting on a centrifuge's tube as it spins are just a few examples.Centripetal forces are any net forces that result in a consistent circular motion.To learn more about Centripetal force, refer to:
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An external force of 34.0 N acts on a system for 12.0 s in the negative x direction. What is the impulse delivered to
the system?
Answer:
90. 6
Explanation:
An external force of 25 N acts on a system for 10 s.
A sprinter Sarting from rest reaches a top speed of 10 m/s im 5 s calculate the average acceleration
Answer:
2 м/с
Explanation:
Скорость надо разделить на время, за которое она достигается (10/5=2)
Which of these ranges of electromagnetic radiation has the shortest wavelengths? A. visible light. B. X-rays. C. infrared radiation. D. ultraviolet radiation
Answer:
Ultraviolet Radiation
Explanation:
UV radiation has the highest frequency/shortest wavelength.
Range Wavelength (nm) [nm = nanometers; 10^-9m]
Ultraviolet 10-400 nm
Violet - 400-420 nm
Indigo - 420 - 440 nm
Blue - 440 - 490 nm
Green - 490 - 570 nm
Yellow - 570 - 585 nm
Orange - 585 - 620 nm
Red - 620 - 780 nm
Visible:
Organic matter such as wood, rice hulls, and sugar cane are all renewable and are examples of _____.
fission produces
nuclear fuels
fossil fuels
biomass
Answer:
d biomass
Explanation:
Estimate the value of the gas-phase diffusion coefficient for the following gas pairs using the Hirschfelder equation
Helium and air
The Hirschfelder equation, D(air-He) = 2.22 x 10-5 cm2/s, can be used to calculate a gas-phase diffusion coefficient of air and helium.
What is Diffusion ?Difussion is a crucial step in the manufacturing of some products, including semiconductors, where it is utilised to create the proper chemical composition. It involves molecules moving from a region of higher concentration to one with a lower concentration. This phenomenon, which is brought about by the random movement of molecules, occurs naturally in all systems. The process of diffusion is crucial for a variety of processes, such as the transmission of heat, the exchange among gases during respiration, and the passage of nutrients through cell.
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According to the law of conservation of mechanical energy, if the only force acting on this pendulum is gravity, the total energy of the system is _____. The same at a, b, and c higher at b than at a and c higher at a and c than at b lost over time.
According to the law of conservation of mechanical energy, if the only force acting on this pendulum is gravity, the total energy of the system is the same at a, b and c.
A, B and C are the three different positions of pendulum bob. A is the left most extreme position. B is the centre position. C is the right most extreme position.
When a pendulum bob is suspended from a rigid support, the extreme positions A and C are said to possess only potential energy where as the centre position of the bob is said to possess only the kinetic energy.
According to the principle of law of conservation of energy in pendulum, the energy can neither be created nor destroyed but can be transformed from one form to another.
Thus, the total energy of the system is the same at all the positions of the pendulum bob.
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What is the power (in Watts) of a bus that uses 35 N of force to move 20 m in 5s?
Power is the rate at which work is done, and it is measured in watts (W). It can be calculated using the formula:
Power = Work / Time
Work can be calculated using the formula:
Work = Force x Distance x cos(theta)
where Force is measured in Newtons, Distance is measured in meters and theta is the angle between the force and displacement vectors.
As we are not giving any value for the angle between force and displacement vectors, we can assume it's zero degree, so the cos(0)=1
So we can plug in the given values to find the work done:
Work = 35 N x 20 m x 1 = 700 J
Now we can calculate power:
Power = 700 J / 5 s = 140 W
Therefore, the power of the bus is 140 Watts
An amusement park ride consists of a rotating circular platform 7.4 m in diameter from which 10 kg seats are suspended at the end of 1.81 m massless chains. When the system rotates, the chains make an angle of 26.6 degree with the vertical. The acceleration of gravity is 9.8 m/s
a). what is the speed of each seat? answer in units of m/s
b). if a child of mass 49.1 kg sits in a seat, what is the tension in the chain ( for the same angle)? answer in units of N
a) The speed of each seat in an amusement park ride of a rotating circular platform is calculated to be 5.57 m/s.
b) The tension in the chain if a child of mass 49.1 kg sits in a seat is calculated to be 650.79 N.
a) By drawing a free body diagram, we represent the two types of forces on the seat. They are represented by the equation, sum of forces in the y direction,
∑F = ma
T cos θ − mg = 0
T = mg / cos θ
Sum of forces in the centripetal direction,
∑F = ma
T sin θ = m v² / r
(mg / cos θ) sin θ = m v² / r
m g tan θ = m v² / r
g tan θ = v² / r
v = √(gr tan θ)
First, let us find the radius of the path,
r = 7.4 / 2 + 1.81 sin 26.6°
r = 3.7 + 1.81× 0.45 = 6.33 m
v = √(9.8 m/s² × 6.33 m × tan 26.6°)
v = √(9.8 × 6.33 × 0.5) = 5.57 m/s
b) T = mg / cos θ
T = (10 kg + 49.1 kg) (9.8 m/s²) / cos 26.6° = 579.2/0.89
T = 650.79 N
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Historically, crash research has required the cooperation and combined knowledge, skills, creativity, and
passion of individuals from many different fields/subject areas. Explain how Col. John Stapp's research
combined several different fields of study to save human lives.
The numerous nails that come into touch with his body while he is heavy and the block are heavy are responsible for much of the force.
How are the forces caused by his weight, the block, and the hit lessened so that he can survive the situation? The numerous nails that come into touch with his body while he is heavy and the block are heavy are responsible for much of the force.Due to this, fewer nails are under pressure.A combination of the vehicle's crash worthiness, an extended impact duration, and driver-energy dissipation.In order to minimize the impact of the force in the collision, the duration is extended. This causes the force to decrease.The force would be ten times smaller if the collision period was simply extended by a factor of 10.The protagonist of The Accident serves as a messenger from the dead to the living, making death the main theme of the novel.He has experienced a living death, having died in part during the HolocaustTo learn more about crash research refer
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A pitcher applies an average force of 6.2 N in the forward direction on a baseball for 0.65 seconds. The baseball’s mass is 0.145 kg. and initial velocity is zero.
What momentum does the baseball have as it is released by the pitcher?
How fast is the baseball going after the impulse?
The catcher catches the baseball in the problem above. It takes 0.15 seconds to stop the ball. How much average force must the catcher apply during that time interval? (Ignore air resistance.)
Answer:
1. The momentum of the baseball as it is released by the pitcher is 0.913 Ns.
2. The velocity of the baseball after the impulse is 9.3 m/s.
3. The average force that the catcher must apply during the 0.15 second time interval is 12.2 N.
Explanation:
1. Momentum = Force x Time = 6.2 N x 0.65 s = 0.913 Ns
2. Velocity = Momentum / Mass = 0.913 Ns / 0.145 kg = 9.3 m/s
3. Force = Change in Momentum / Time = (0.913 Ns - 0) / 0.15 s = 12.2 N
if a cars engine is 27.5 effeicient at converting the fuels energt ubti necgabucal eberft if 1L of gasoline has 33.5J of input energy how much useful energy output will 2.50L of fuel provide
The efficiency of the engine is given 27.5%. The input energy of 2.5 L gasoline is 83.75 J. Then, the energy output will be 23.01 J.
What is engine efficiency ?The efficiency of an engine is the ratio of its output work done to the energy input. No engine can have 100% efficiency. Hence, some energy is lost in the form of heat.
Given that, the efficiency of the car's engine is 27.5 %. Input energy of 1 L gasoline is 33.5 J. Then, energy input for 2.5 l is:
input energy = 2.5 × 33.5 = 83.75 J.
Engine efficiency = energy output/ input energy × 100
O/ 83.75J × 100 = 27.5 %
O/83.75 = 0.275
then output energy = 83.75 × 0.275 = 23.01 J.
Therefore, the energy output of the fuel is 23.01 J.
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Analyze the IR spectra for both t-butanol and 1-butanol.
If the reactions were successful what do you expect to see in the IR of the product compared to the starting material?
If the reactions were successful then we can see the reactions involved O-H groups of the alcohols then the O-H stretching will not be observed in the product.
Analysis of IR spectrum of 1-butanol:
There are sp3 C-H stretching and CH2 bending modes at 2900 and 1500 cm-1 and there is a C-O stretching mode near 1050 cm-1. There is a very large peak around 3400 cm-1. O-H peaks are usually very broad due to H -bonding.The rounded shape O-H stretching modes occurs because of hydrogen bonding between different hydroxy groups.
Because protons are shared to varying extent with neighboring oxygens, the covalent O-H bonds in alcohol all vibrate at slightly different frequencies and show up at slightly different positions in the IR spectrum.
Instead of seeing one sharp peak, the entire range is observed as a whole lot of them merged into one broad peak. Since C-H bonds don't hydrogen bond very well, hence this phenomenon is not observed for C-H stretching.
Analysis of IR spectrum of tertiary-butyl alcohol:
There are sp3 C-H stretching and alkane C-H bending modes at 2900 and 1500 cm-1 and there is a strong C-O stretching mode near 1200 cm-1 indicative of tertiary C-O, there is a broad peak around 3400 cm-1 indicative of H bonding.
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