An amusement park ride consists of a large vertical wheel of radius R and a horizontal axis through its center that revolves counterclockwise.
What is an amusement ride?Amusement rides, often known as carnival rides, are machines or installations that move people for entertainment and fun.
Many people mistakenly believe that rides are scarier or more dangerous than they actually are. This can be the result of the design, acrophobia, or knowledge of accidents involving similar rides. Some people enjoy the adrenaline rush that comes with riding amusement attractions since it adds to the experience.
amusement rides such as ferris wheels, Enterprise, and Skydiver are examples of vertical rides that typically move their guests in a vertical plane and around a fixed point.
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A cement block accidentally falls from rest from the ledge of a 59.7-m-high building. When the block is 15.1 m above the ground, a
man, 1.80 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the
way?
The maximum time necessary for the man to get out of the way is 1.65 seconds.
How much time does the man have to get out of the way?
The maximum time necessary for the man to get out of the way in order to safe is calculated as follows;
h = vt + ¹/₂gt²
where;
v is the initial velocity of the blockt is the time of motion of the blockg is acceleration due to gravitythe height above the man's head = 15.1 m - 1.8 m = 13.3 m
h = 0 + ¹/₂gt²
t = √ ( 2h / g )
t = √ ( 2 x 13.3 / 9.8 )
t = 1.65 seconds
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Two students are discussing the motion of the dart-block system at the instant it reaches height H. The students make the following statements:Student 1: The speed of the system at height H is zero. Since it is moving in circular motion and centripetal acceleration is given by ac = v2 , the acceleration must also be zero.Which underlined phrase or phrases, if either, are correct about student 1's statement? If neither phrase is correct, write "none."
The underlined phrase "The speed of the system at height H is zero", "Since it is moving in circular motion and centripetal acceleration is given by ac = v², the acceleration must also be zero" are both underlined phrases are not correct about student 1's statement.
The underlined phrase "The speed of the system at height H is zero" is not correct about student 1's statement. The statement is incorrect because at the instant it reaches height H, the system would have lost some of its initial kinetic energy due to gravity and would be moving with some velocity, though it could be very small.
The underlined phrase "Since it is moving in circular motion and centripetal acceleration is given by ac = v², the acceleration must also be zero" is also not correct about student 1's statement. The statement is incorrect because the centripetal acceleration is not given by ac = v², but rather ac = v2/r, where r is the radius of the circular path.
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Consider a rigid steel beam of length L= 10.5m and mass mb= 375 kgresting on two supports, one at each end. A worker of mass mw= 61kg sits on the beam at a distance x from support A. Refer to thefigure.A. Enter an expression for the force support B must exert on the beam in order for it toremain at rest, in terms of defined quantities and g.a. FB=g(xmW/L + mB/2)
The force support B must exert on the beam in order for it to remain at rest is equal to the sum of the forces caused by the beam's weight (mg) and the worker's weight (mw).
What is force?Force is a physical quantity that is used to describe an interaction between two objects. It is a vector quantity, meaning that it has both magnitude and direction. Force can cause an object to accelerate, decelerate, change shape, or even change direction. It is a measure of how much energy is transferred between two objects, and can be calculated using the equation: Force = mass x acceleration.
For equilibrium, the sum of the forces must be zero. Therefore, the force Support B must exert on the beam is equal to the sum of the forces acting on the beam, which can be expressed as FB = g(xmW/L + mB/2). Here, g is the acceleration due to gravity, mW is the mass of the worker, mB is the mass of the beam, and L is the length of the beam.
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Two rivers have the same volume of water flow over time but fall from different heights to power hydroelectric turbines. Which river would provide the most power? Explain why you chose that answer, describing the water's kinetic energy, potential energy and the law of conservation of energy.
( Giving 20 points )
The river at the greatest height will possess more potential energy and provide power when it falls on the turbine.
What is potential energy?The potential energy of an object is the energy possessed by the object due to its position above the ground level.
The river at a higher position will possess more potential energy and based on the law of conservation of energy, the higher potential energy of the river will be converted into more kinetic energy, causing the turbine to rotate more to generate more electricity and provide the most power.
Thus, the law of conservation of energy will allow the potential energy of the river to be converted into kinetic energy of falling water and the electricity from the turbine.
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Two wires, A and B, and a variable resistor, R, are connected in series to a battery. Which one of the following results will occur if the resistance of R is increased?
If two wires, A and B, and a variable resistor, R, are connected in series to a battery, and resistance of R is increase, hence the total current through the battery will increase and the current through the entire circuit will decrease (option E)
The relationship between the voltage applied and the quantity of current flowing through something is known as the electrical resistance. In other words, we can argue that an electrical circuit's ability to resist the flow of current through it is one of its characteristics. The relationship between voltage, current, and resistance is given by Ohm's law. i.e.
V = IR
Where
V = the voltage.
I = the current.
R = the resistance (Omega / Ω)
Because the network's equivalent resistance has decreased, the current flowing through the battery will increase (current = voltage/resistance).
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An example of using sustainable practices in creating new products would be ______
a large company installs low-flush toilets in all of its plant and warehouse loca
an office building stops using paper products and asks workers to bring their
a tile company collects and recycles old tiles from large facilities and makes m
a large data center uses computer modeling to get rid of hot spots that waste
Answer:
"a tile company collects and recycles old tiles from large facilities and makes m"
Explanation:
While the first two sound sustainable, and they are, they're not necessarily part of creating new products. The third option where "a tile company collects and recycles old tiles from large facilities and makes m" which is cut off although I'm assuming "makes more?" making it part of the process of creating new products, although it's more sustainable as it uses old products.
g the molar heat capacity of diamond changes with temperature, but for temperatures lower than 500 k k it is reasonably well modeled as being proportional to t3 3 ; that is, c
Where A is a constant, V (T) equals AT3. Diamond's molar heat capacity is temperature dependent, and the calculation you supplied is a typical technique to predict how it will behave at low temperatures.
How much molar heat can a diamond hold?The molar heat capacity of diamond, however, is smaller than that of an ideal gas and is approximately 6.11 J/(molK).
Why does diamond melt when the temperature is high?Every single C-C bond has an extremely high bond energy. To enhance the intermolecular separation and melt the diamond, these bonds must be disrupted. Diamond melts at a very high temperature because high temperatures are needed to dissolve such powerful connections.
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find its instantaneous velocity at point a . express your answer in meters per second to two significant figures.
The instantaneous velocity of an object may be equal to its standard velocity if it has uniform velocity.
What is instantaneous velocity?The definition of instantaneous velocity is the rate of change of position over a relatively brief time period (almost zero). m/s, the SI unit of measurement. The size of the immediate velocity is known as the instantaneous speed. Although it lacks a direction, it has the same value as instantaneous velocity.
Simply said, the speed of an object at that precise moment. The definition of instantaneous velocity is "The velocity of an item in motion at a certain point in time."
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The illustration shows a light ray striking an object. In the illustration, the light ray striking the object is reflecting. What is most likely true about the
object?
A
The object has a rough surface.
The object has an uneven surface.
Nothing can be determined about the surface of the object.
The object has a smooth surface.
Light traveling in air strikes a flat piece of uniformly thick glass at an incident angle of 60.0, as shown in the figure on the right. If the index of refraction of the glass is 1.50
, what is the angle of refraction in the glass, what is the angle at which ray emerges from the glass?.
Answer:
the angle at which the ray emerges from the glass is approximately 26.8°.
Explanation:
Assuming that the angle of incidence is measured from the normal, the angle of incidence of the light ray in air is 60.0°. Using Snell's law, we can find the angle of refraction in the glass:
n1 sinθ1 = n2 sinθ2
where n1 is the refractive index of air, which is approximately 1, and n2 is the refractive index of the glass, which is given as 1.50. Therefore, we have:
1.00 sin 60.0° = 1.50 sinθ2
θ2 ≈ 40.9°
So the angle of refraction in the glass is approximately 40.9°.
To find the angle at which the ray emerges from the glass, we need to apply Snell's law again using the angle of incidence in the glass and the refractive index of air:
n2 sinθ2 = n1 sinθ3
where θ3 is the angle of refraction in air. Plugging in the values, we get:
1.50 sin 40.9° = 1.00 sinθ3
θ3 ≈ 26.8°
So the angle at which the ray emerges from the glass is approximately 26.8°.
object a has a charge of 12 c, and object b has a charge of 16 c. which statement is true about the electric forces on the objects? (a) f : ab 5 23f : ba (b) f : ab 5 2f : ba (c) 3f : ab 5 2f : ba (d) f : ab 5 3f : ba (e) f : ab 5 f : ba (f) 3f : ab 5 f : ba
The statement regarding the electric forces on the objects is true: f: ab 5 2f: ba.
What alteration boosts the electric force?As the space between two charged items grows, so do the electric forces between them. With more charge on the objects, there are greater electric forces between the charged things. Each object's charge has a direct impact on electrostatic force. Therefore, if the charge of one object is doubled, the force will increase by two times.
What may be said to be true about force?There is either a push or a pull. The effects of forces include moving an object, altering its speed, altering its shape, or changing the volume of a body.
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What is the acceleration of a 2,500-kg single-engine airplane just before takeoff when the thrust of its engine is 500N?
The acceleration of a 2,500-kg single-engine airplane just before takeoff when the thrust of its engine is 500N is, 0.2 m/s²
What is acceleration ?Acceleration is a vector quantity that describes the rate at which an object changes its velocity. It is the rate at which the velocity of an object changes in magnitude or direction, or both. In other words, it tells us how quickly an object is speeding up or slowing down. Acceleration has units of meter per second squared (m/s²) and its direction is the same as the direction of the change in velocity.
The net force acting on the airplane just before takeoff is equal to the thrust of the engine,
which is 500 N, minus the force of drag.
Since the airplane is just about to take off, the force of drag is relatively small,
So we can assume that the net force is equal to the thrust of the engine.
F = m x a
Where F is the net force, m is the mass, and a is the acceleration.
Substituting the values for F and m, we get:
500 N = 2,500 kg x a
Dividing both sides by 2,500 kg, we get:
a = 500 N / 2,500 kg = 0.2 m/s²
So, the acceleration of the 2,500-kg single-engine airplane just before takeoff when the thrust of its engine is 500 N is 0.2 m/s².
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Suppose that there is a uniform electric field that points in the +x direction. If the electric potential is 5.44 volts at x=9.71 and 6.84 volts at x=9.36, what is the magnitude of this electric field in N/C?
The magnitude of this electric field is 0.37 N/C.
What is a "electric field"?An electric field is associated with a location in space whenever charge of any type is present there. The electrostatic potential's magnitude and orientation are described by the value of E, often known as the electric field strength, electric field, or simply the electric field.
Using the formula:
E = ΔV/Δx
where x represents the change in motion and V represents the difference in potential.
ΔV = 5.67 V - 3.46 V = 2.21 V
Δx = 9.72 m - 3.79 m = 5.93 m
Putting in the values, we get:
E = ΔV/Δx = 2.21 V / 5.93 m
= 0.37 V/m =
0.37 * (1 N/C) / (1 V)
= 0.37 N/C
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JustAnswer JustAnswer
the answer it letter b for your question
A system is a simple compressible system in the absence of _____ and surface tension effects. (Select all that apply.)
-electrical
-motion
-gravitational
-magnetic
A system is a simple compressible system in the absence of electrical, motion, gravitational, magnetic and surface tension effects.
In thermodynamics, the term "state postulate" describes a set of properties that apply to a system that has achieved thermodynamic equilibrium, also It's a known as "the state principle". The state postulate stipulates that only a limited set of attributes need to be given in order to provide an exhaustive account of a state of thermodynamic equilibrium. After the state postulate has been established, the other undefined attributes are required to take on certain values.
State postulate claims "The state of a simple compressible system is completely specified by two independent, intensive properties". A system is said to as a simple compressible system in the absence of electrical, magnetic, gravitational, motion, and surface tension effects. These effects are caused by external force fields and are insignificant for the majority of engineering problems.
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80m E 20m S FIND THE AIR SPEED OF THE PLANE RELATIVE TO THE GROUND.
The air speed of an airplane traveling 80 meters east and 20 meters south in a second relative to the ground is about 82.46 m/s
What is the airspeed of a plane relative to the ground?The air speed of a flying airplane relative to (a specified location on) the ground is the difference between the airplane's ground speed and the speed of the wind, found using vectors as follows;
Mathematically, we get;
Airspeed = Ground Speed - Wind SpeedWhereby the velocity of the wind is 120 m/s and the airplane is traveling with an airspeed of 300 m/s due east for example, and the airplane travels 80 meters east and 20 meters south relative to the ground in one second, we get;
Resultant valocity = 80 m/s East, 20 m/s South
v = 80·i - 20·j
The magnitude of the velocity of the plane relative to the ground can be found, using the formula for the magnitude of resultant vector as follows;
|v| = √(80² + (-20)²) = 20·√(17) ≈ 82.46
The air speed of the plane relative to the ground is therefore;
|v| ≈ 82.46 m/s
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Which of the following changes to the Earth's sun system would reduce the magnitude of the force between them to 1/4 The value found in part a
When the distance between earth and sun becomes double, the force between them reduces to 1/4th.
What is gravity?Gravity is a fundamental interaction in physics that causes all objects with mass or energy to attract one another. The weakest of the four fundamental interactions is gravity, by a wide margin.
At the macroscopic level, gravity is the most important interaction between things and governs the motion of planets, stars, galaxies, and even light.
When the distance between earth and sun becomes double, the force between them reduces to 1/4th.
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When a rattlesnake strikes, its head accelerates from rest to a speed of 22 m/s in 0.63 seconds. Assume for simplicity that the only moving part of the snake is its head of mass 120 g.
How much (average) power does the rattlesnake need to accelerate its head that fast?
Answer in units of W. Answer in units of
W.
Answer:183
Explanation:when you have taken 120g and 22m/s in 0.63 the acceleration has the speed of 183
A 53-years old lady was found by imaging to have 50% narrowing in her left renal artery. The change in blood flow for that artery is: (poiseuille Law)
A. 1⁄3 reduction in flow
B. 1⁄2 increase in flow
C. 1/16 increase in flow
D.1/16 reduction in flow
Answer:
D. 1/16 reduction in flow
Explanation:
Poiseuille's law says that the flow rate in a tube or pipe is:
[tex]Q=\frac{\pi P r^4}{8 \eta L}[/tex]
where P is the pressure difference, r is the radius, η is the viscosity, and L is the length.
Assuming that P, η, and L are constant, then we can say Q is proportional to r⁴.
Q ∝ r⁴
A 50% narrowing means the new radius is r/2. Thus the new flow is:
Q₀ / r⁴ = Q / (r/2)⁴
Q₀ / r⁴ = 16 Q / r⁴
Q = Q₀ / 16
There is a 1/16 reduction in flow.
In the schematically drawn circuit shown below, a light bulb is connected in series with a resistor. What is the total resistance in the circuit?
A) 90 ohms
B) 80 ohms
C) 100 ohms
D) 4 ohms
According to the values of all the resistors in the circuit and their connections, a circuit's overall resistance can be calculated (in series, in parallel, or a combination of both).
How much resistance does the circuit in its whole have?In a series circuit, the sum of each component resistance determines the circuit's overall resistance. The current in a series circuit is the same size everywhere it is present because there is only one channel for electrons to follow.
How much resistance does each parallel resistor add up to?The total resistance for resistors connected in parallel is equal to the reciprocals of each resistor added together.
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Help with Part 1 and 2
I want to check my work and graph
The point t = 0 to t = 8 depict the acceleration of the object.
What is acceleration?Acceleration is a measure of the change in velocity of an object over time. It is a vector quantity that describes the rate at which an object changes its speed or direction of motion. Acceleration is calculated as the rate of change of velocity, and is expressed in units of meters per second squared (m/s²).
We can see from the graph that between t = 0 and t =8 was the time that the object underwent acceleration.
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On a post flight inspection of your aircraft after an aborted takeoff due to an elevator malfunction, you find that the elevator control cable has broken. According to NTSB 830, you
a) must immediately notify the nearest NTSB office
b) should notify the NTSB within 10 days
c) must file a NASA report immediately
You must promptly inform the nearby NTSB office that the elevator control cable has broken, per NTSB 830.
When should the NTSB be notified of an aviation accident if there was significant damage but no injuries?The operator is required to submit a report using NTSB Form 6120.1 or 6120.2, which can be obtained from NTSB Field Offices or the NTSB in Washington, D.C. 20594: ten days following an accident.
What qualifies as an accident in the NTSB's eyes?Any incident involving the operation of an aircraft that occurs between the time a passenger boards with the intention of taking off and the time they have all disembarked and in which a person is killed or seriously injured is referred to as an aircraft accident.
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A student sets up a circuit like the one shown below and wants to measure the following:
the current in the circuit
the potential difference across the lamp
the electromotive force of the cell
How many ammeters and how many voltmeters does the student need to use?
Group of answer choices
A) 1 ammeter and 2 voltmeters
B) 2 ammeters and 1 voltmeter
C) 3 ammeters and 0 voltmeters
D) 0 ammeters and 3 voltmeters
Answer:
see below
Explanation:
To measure the current in a circuit we need an ammeter. it is connected in series in the circuit.
To measure potential difference across the lamp you will need a voltmeter. A voltmeter is connected in parallel in circuit.
To measure emf you would again need a voltmeter.
So we need one ammeter and 2 voltmeter .
Additional information:-
An ammeter and a voltmeter both are made from galvanometer . To measure current a device should have minimum resistance, so for this a low resistance called shunt is connected in parallel with the galvanometer to make it a ammeter. Since in parallel combination of resistors,
[tex]\implies R_{net} < R_1 / R_2 / R_3 / .. \\[/tex]
To measure potential difference, there should be least current flowing through the device, so we add a high resistance in series with galvanometer to make it voltmeter.
and we are done!
The student will need 1 ammeter and 2 voltmeters.
Option A is correct.
What is an ammeter?An ammeter is described as an instrument used to measure the current in a circuit.
An ammeter and a voltmeter both are made from galvanometer . In order to measure current, a device should have minimum resistance, so for this a low resistance called shunt is connected in parallel with the galvanometer to make it an ammeter.
Below are some of the types of ammeter:
1-Moving coil Ammeter.
2-Moving magnet Ammeter.
3-Electrodynamic Ammeter.
4-Moving iron Ammeter.
5-Hot wire Ammeter.
6-Digital Ammeter.
7-Integrating Ammeter.
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Two small objects are suspended from threads. When the objects are moved close together, they attract one another. Which of the following could produce this result?A) One object is positively charged and the other is negatively charged.B) One object is positively charged and the other is uncharged.C) One object is negatively charged and the other is uncharged.D) All of the above could result in such attraction.
When two objects are suspended from wires, All of the above can result in such an attraction. The correct answer D.
When two objects are suspended from threads, the movement of one object close to the other can cause the electrons in the atoms of one object to be transferred to the other, resulting in one object gaining a positive charge and the other gaining a negative charge.
This causes the two objects to attract each other due to the opposite charges.
This phenomenon is known as electrostatic attraction, and it occurs due to the electrostatic force of attraction between charged objects. The strength of this force depends on the distance between the objects and the magnitude of their charges. When the objects are brought closer together, the force of attraction becomes stronger, and they may even stick together.
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what relationship between the total mechanical energy and gravitational potential energy universal gravitation
In a system under the influence of universal gravitation, the total mechanical energy of an object is the sum of its kinetic energy and its gravitational potential energy. The total mechanical energy of an object is conserved if the only force acting on it is the force of gravity.
Gravitational potential energy is a type of potential energy that an object possesses as a result of its position relative to other objects in a gravitational field. It is proportional to an object's mass, the acceleration due to gravity (g), and its height above the reference point.
The formula for gravitational potential energy is given by:
U = mgh
where U is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the reference point.
So, the total mechanical energy E of an object in a gravitational field can be expressed as:
E = kinetic energy + gravitational potential energy [tex]= 1/2mv^2 + mgh[/tex]
where m is the mass of the object, v is its velocity, and h is its height above the reference point.
In short, the relationship between the total mechanical energy and gravitational potential energy in a system under the influence of universal gravitation is that the total mechanical energy of an object is equal to the sum of its kinetic energy and its gravitational potential energy.
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A 5.2 "kilo" bag of sugar is on a counter. How much work is required to put the bag on a shelf a distance of 0.37 m above the counter?
Answer:
approximately 18.854 Joules of work is required to put the bag of sugar on the shelf.
Explanation:
The work required to lift the bag of sugar to a height of 0.37 m against the force of gravity can be calculated as:
Work = Force x Distance
where Force is the weight of the bag of sugar and Distance is the vertical distance lifted.
The weight of the bag of sugar can be calculated as:
Weight = Mass x Gravity
where Mass is the mass of the bag of sugar and Gravity is the acceleration due to gravity.
Given that the bag of sugar weighs 5.2 kilograms, the weight of the bag of sugar can be calculated as:
Weight = 5.2 kg x 9.81 m/s^2 = 50.932 N
The distance lifted is 0.37 m.
Therefore, the work required to lift the bag of sugar to a height of 0.37 m can be calculated as:
Work = Force x Distance = 50.932 N x 0.37 m = 18.854 J
Thus, approximately 18.854 Joules of work is required to put the bag of sugar on the shelf.
one of the absorption lines of hydrogen has a rest wavelength of 656 nm (at rest means with respect to the observer, like in a lab). You observe several stars and measure the wavelength of this same hydrogen absorption line in each star. Based on the measured wavelength of this line, which star is moving towards the Earth the fastest?
Star with the measured wavelength of 652 nm is moving towards the Earth the fastest.
What is doppler effect?The wavelength of light from a moving source is shifted due to the Doppler effect. If a star is moving towards the Earth, wavelength of the light it emits is shifted to shorter (bluer) wavelengths and if it is moving away from the Earth, wavelength is shifted to longer (redder) wavelengths.
As, Δλ/λ = v/c
Δλ is shift in wavelength, λ is rest wavelength, v is speed of the star relative to the Earth, and c is the speed of light.
Let's say we measure a wavelength of 654 nm for one star, and 652 nm for another star. Then, we can calculate the shift in wavelength as follows:
Δλ/λ = (656 nm - 654 nm) / 656 nm = 0.00305
Δλ/λ = (656 nm - 652 nm) / 656 nm = 0.0061
We see that the star with measured wavelength of 652 nm has larger shift in wavelength and therefore is moving towards the Earth faster than star with the measured wavelength of 654 nm.
So, the star with the measured wavelength of 652 nm is moving towards the Earth the fastest.
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Lightning A cloud has a large positive charge. Assume that this is the only cloud in the sky over Earth and that Earth is a good electrical conductor. Draw a sketch showing elec- tric charge distribution on Earth due to the cloud’s electric charge. Explain why a person’s hair might stand on end be- fore a lightning strike.
The cloud has a positive charge. This positive charge entices a negative charge in the Earth. So the part of Earth that is close to the cloud has a negative charge and the distant part has a positive charge.
A person on earth has electric charges, like the Earth. On the end, before lightning strike cloud and earth have the utmost charge that they can carry. So in this time, the person has a large stake of charge like when he or she skims a Van De Graaff. The hair is placed on end when strands have the exact charge because of the repulsive electric force between them. Likewise, before the lightning strike, the person's hair might be placed on end.
Therefore, before a lightning strike person has a great stake of charge like when he or she adjoins a Van De Graaff.
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A diagram showing electric charge distribution on Earth due to the cloud's electric charge.
Which of the following does not generate a magnetic field?
A. a moving electric charge
B. an electric current in a straight wire
C. an electric current in a wire loop
D. a stationary electric charge
Answer:
D
Explanation:
Stationary electric charges produce electric field, it's expression is given by Coulomb's Law. Moving electric charges produce electric field, it's expression is given by a more complicated form than the Columb's Law. Stationary electric charges DOES NOT produce magnetic field.
question 1: approximating small oscillations (grader a, 15 points) a particle of mass m is constraint to move along x. its potential energy is u(x)
The angular frequency of small oscillations about the minima of the potential energy U(x)=−ax^2 +bx^4 is equal to 2√a/m
Given the potential energy U(x) = −ax^2 +bx^4
Differentiate the given potential energy such that:
dU/dx = d/dx(−ax^2 +bx^4)
dU/dx = -2ax + 4bx^3
x(4bx^2 −2a) = 0
Then x1 = 0 and x2 = √a/2b
We know the force acting = F = -kx
dF/dx = k = d2/dx2(U)
k = d/dx( -2ax + 4bx^3 )
k = -2a + 12bx^2
k(x=0) = -2a
k(x=√a/2b) = 4a
We know the angular frequency (ω) = √k/m = √4a/m = 2√a/m
Hence, the angular frequency of small oscillations about the minima of the potential energy is equal to 2√a/m
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complete question: A particle of mass m moves in a one-dimensional potential energy U(x)=−ax^2 +bx^4, where 'a' and 'b' are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to