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Find total response of the system (transient+steady state). Do not solve for coefficients. Determine the frequency of applied force at which resonance will occur? M = 20 kg F, = 90 N Given: -6 rad/s M
Given the following information:Mass of the system, m = 20 kg.Damping coefficient, b = 6 Ns/m.Force, F = 90 N.Frequency of applied force, f = ?Applied force angular frequency, w = 6 rad/s.Forced vibration equation:F(t) = F0 sin(wt)where F0 = 90 N and w = 6 rad/s.Under the action of the force F, the mass m will oscillate.The equation of motion for the mass-spring-damper system is given by:$$\mathrm{m\frac{d^{2}x}{dt^{2}}} + \mathrm{b\frac{dx}{dt}} + \mathrm{kx = F_{0}sin(\omega t)}$$where k is the spring constant.x(0) = 0 and x'(0) = 0.As we have the damping coefficient (b), we can calculate the damping ratio (ζ) and natural frequency (ωn) of the system.Damping ratio:$$\mathrm{\zeta = \frac{b}{2\sqrt{km}}}$$where k is the spring constant and m is the mass of the system.Natural frequency:$$\mathrm{\omega_{n} = \sqrt{\frac{k}{m}}}$$where k is the spring constant and m is the mass of the system.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$At resonance, the amplitude of the system will be maximum when forced by a sinusoidal force of frequency equal to the resonant frequency.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$$$\mathrm{\omega_{d} = \sqrt{(6.57)^{2}-(-2.88)^{2}} = 6.98 rad/s}$$Hence, the frequency of applied force at which resonance will occur is 6.98 rad/s.
The frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.
To determine the frequency of the applied force at which resonance will occur, resonance happens when the frequency of the applied force matches the natural frequency of the system. The natural frequency can be determined using the formula:
ωn = √(K / M),
where ωn is the natural frequency, K is the spring constant, and M is the mass of the system.
Substituting the given values of K = 400 N/m and M = 20 kg into the equation, we can calculate the natural frequency ωn.
ωn = √(400 N/m / 20 kg) = √(20 rad/s²) = 2√5 rad/s.
Therefore, the frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.
The correct question is given as,
M= 20kg
Fo = 90 N
ω = 6 rad/s
K = 400 N/m
C = 125 Ns/m
Determine the frequency of applied force at which resonance will occur?
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Which type of electromagnetic radiation is most likely to be non -ionizing radiation ? A. Radio B. Ultraviolet C. X -rays D. Gamma rays
Radio waves are most likely to be non-ionizing radiation.
Electromagnetic radiation can be classified into ionizing or non-ionizing radiation, depending on its ability to ionize atoms or molecules in its path. Ionizing radiation has enough energy to remove electrons from atoms or molecules, while non-ionizing radiation lacks sufficient energy to do so.
Radio waves have the lowest frequency and energy among the different types of electromagnetic radiation in the electromagnetic spectrum. They have a wavelength range of 1 millimeter to 100 kilometers, and their energy is typically below 10^-4 electron volts, which is not enough to ionize atoms or molecules. As a result, radio waves are classified as non-ionizing radiation.
On the other hand, ultraviolet, X-rays, and gamma rays have higher frequencies and energies than radio waves and are classified as ionizing radiation. Ultraviolet radiation has enough energy to ionize atoms or molecules in the air, causing sunburn and other skin damage. X-rays and gamma rays have enough energy to penetrate through materials, including human tissues, and can cause cellular damage or mutations if exposure occurs.
In summary, radio waves are non-ionizing radiation, while ultraviolet, X-rays, and gamma rays are ionizing radiation.
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Why does the first row in our periodic table
only have two elements?
A) because each orbital in every sub-level only holds
two electrons
B) because Bohr only knew about two elements
C) because the first energy level only holds two
electrons total
Help me plssss
Answer:
B
Explanation:
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Answer:
C option is correct
Explanation:
C) because the first energy level only holds two electrons.
What is the electrical force of two punctiform electrical charges of 3ųC and 4ųC respectively at a distance of 10 cm in a vacuum
Answer:
Electrical force, F = 10.8 N
Explanation:
We have,
Charge 1, \(q_1=3\ \mu C=3\times 10^{-6}\ C\)
Charge 2, \(q_2=4\ \mu C=4\times 10^{-6}\ C\)
Distance between charges is 10 cm or 0.1 m
It is required find the electric force between two charges. The formula used to find the electrical force is given by :
\(F=\dfrac{kq_1q_2}{r^2}\)
k is electrostatic constant
Plugging all the values we get :
\(F=\dfrac{9\times 10^{9}\times 3\times 10^{-6}\times 4\times 10^{-6}}{(0.1)^2}\\\\F=10.8\ N\)
So, the electrical force between charges is 10.8 N.
Define potential difference in a uniform electric field?
Explanation:
For example, a uniform electric field E is produced by placing a potential difference (or voltage) ΔV across two parallel metal plates, labeled A and B. ... The relationship between ΔV and E is revealed by calculating the work done by the force in moving a charge from point A to point B.
If two objects collide and are stationary, what must the total momentum of the sum of the objects have been before collision?
Explanation:
Concept: In collision between two isolated bodies momentum is always conserved.
Also, if the collision is elastic kinetic energies are also conserved
m1v1i + m2v2i = m1v1f + m2v2f.
and in elastic collision
\(½m1v1i^2 + ½m2v2i^2 = ½m1v1f^2 + ½m2v2f^2.\)
Momentum is preserved in collisions between two objects. The initial moment not being zero, the final momentum is not zero. This means both object has to be in motion.
However, it may be possible for one of the objects to be at rest after the collision. For instance, if the masses of the two objects are same, then after a head-on elastic collision the object initially at rest is moving and the object initially moving is at rest.
A student is standing 8 m from a roaring truck engine that is measured at 20. The student moves 4 m closer to the engine. What is the measured sound intensity at the new distance?.
By knowing how intensity relates to distance, we will see that at 4 meters of the engine the intensity is 80.
How sound intensity relates to distance?
The sound spreads in a solid angle like all waves, so the intensity of the sound will decrease with the distance squared, this means that:
\(I = \frac{P}{4*pi*r^2}\)
Where P is the sound power, we know that when the student is at 8m from the engine, the intensity measured is 20 (it does not tell the units) so we have:
\(20 = \frac{P}{4*3.14*(8m)^2} \\\\P = 20*4*3.14*(8m)^2 = 16,078.8 m^2\)
Now, if you move 4 meters closer to the engine, your new position will be:
r = 4m
Then we have:
\(I = \frac{16,078.8 m^2}{4*3.14*(4m)^2} = 80\)
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Answer:
80 is the answer! 100% CORRECT!
Explanation:
~Hope this helps! :)
Ya sabes que los materiales se utilizan dependiendo de la fun- ción que deben tener: transparentes (cristales), conductores de la electricidad (cables de tendidos eléctricos), muy resistentes (vigas), inoxidables (cuberterías), etc. Pero, ¿interesarán materiales de densidad grande o pequeña? ¿Por qué? Busca ejemplos de tres materiales que justifiquen tu respuesta (por ejemplo, el hilo conductor de las líneas de alta tensión, los colchones de espuma de alta densidad, la fibra de carbono, etc). ¿Qué características tiene la fibra de carbono en cuanto a resis- tencia y densidad? Busca objetos que se elaboren con fibra de carbono.
Which of the five zones shown on the map has the greatest amount of land area suitable for people to live?
I have to get it done right now... I'm not playing no games.. I need help with this ASAP
The zone in the map that has the greatest amount of land area suitable for people to live is zone B.
What is equator?The equator is the imaginary line that divides the earth horizontally into two equal halves of North and South zones.
The countries that are located close to the equator include the following:
Ecuador, Colombia,
Brazil, Sao Tome & Principe, Gabon, Republic of the Congo, Democratic Republic of the Congo,Uganda, Kenya, Somalia, Maldives, Indonesia and Kiribati.From the map, the zone with the greatest amount of land area suitable for people to live is the zone closest to the equator which is zone B.
The temperature of these areas are close to moderate through out the year.
The zone B also contains land mass that is part of the largest continent which is Asia.
Therefore, the zone in the map that has the greatest amount of land area suitable for people to live is zone B.
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What is the difference between zone coverage and man coverage, and how can the offense team read those coverages?
Answer:
zone coverage is about sensing what the offense is attempting to accomplish against the defense. Each defensive player reacts when the ball is in the air, whereas in man-to-man coverage, he simply plays the receiver.
Explanation:
how is heat capacity ratio determined experimentally
Heat capacity ratio is determined experimentally by measuring the change in temperature of a gas in response to the addition or removal of heat.
The heat capacity ratio, also known as the adiabatic index, is defined as the ratio of the heat capacity at constant pressure to the heat capacity at constant volume.
To experimentally determine the heat capacity ratio, a sample of gas is subjected to changes in temperature while its pressure and volume are carefully monitored. The change in temperature can be caused by adding or removing heat, or by changing the pressure of the gas through a piston or other mechanism.
The heat capacities at constant pressure and constant volume can then be calculated from the data, and the heat capacity ratio can be determined as their ratio. This measurement can provide valuable information about the thermodynamic properties of gases and can be used to better understand their behavior in different conditions.
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A graph with vertical axis Energy Unit and horizontal axis Amplitude Unit. A line goes in straight segments from 1 16 to 2 9 to 4 1.
Tara prepared a report to show how the amplitude of waves affects the energy of waves. Is her graphical representation correct? Why or why not?
The graphical representation of Tara is correct because of energy of the wave depends on the amplitude of the wave.
Energy of a waveThe energy of a wave due to the motion of a spring is calculated as follows;
E = ¹/₂KA²
where;
k is the force constant of the springA is the amplitude of the waveThus, the graphical representation of Tara is correct because of energy of the wave depends on the amplitude of the wave.
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Answer: No, it is not correct because as the amplitude of a wave increases, the energy it carries also increases. This graph shows that as the amplitude increases, the energy decreases.
Explanation:
a rectangular 4m x 10m swimming pool is filled to a depth of 5 m. what is the force on the bottom of the pool?
The force at the bottom of the pool with its area and depth specified is 1962* 10³ N.
Given that,
Area of the swimming pool = 4* 10 = 40 m²
Depth of the swimming pool = 5 m
We know the formula for pressure as, P = ρ* g * h
where, ρ is the density of water
g is the acceleration due to gravity
h is the depth of the pool
So, P = 1000* 9.81* 5 = 49,050 N/m²
Now, let us calculate force,
Force = Pressure* Area = 49,050 * 4* 10 = 1962* 10³ N
Thus, the force at the bottom of the swimming pool is 1962* 10³ N.
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How do you think organisms capture and store energy? How do you think organisms use and release this energy?
A seller on the internet claims to have pieces of a wooden statue that are 2000 years old. You are asked to date the wood to see whether the age is correct. The 20g sample you receive has an activity of 15 counts per second. For living wood. 20g would have an activity of 16 counts per second. Estimate the age of the wood and women’s on weather the sellers claims are true
Which friction requires the least amount of force to overcome fluid friction or sliding friction?
Fluid friction requires less force to overcome than sliding friction. Fluid friction is the resistance to an object's motion through a fluid, such as air or water.
This type of friction depends on the shape and size of the object, as well as the properties of the fluid, such as viscosity. In general,
with streamlined shapes experience less fluid friction than those with irregular shapes.
Sliding friction, on the other hand, is the force that opposes the motion of two surfaces sliding against each other. This type of friction is caused by the irregularities on the surfaces that come into contact,
which resist the motion of one surface over the other. Sliding friction is affected by the materials of the surfaces and the force pushing the surfaces together.
In terms of the force required to overcome these types of friction, fluid friction requires less force than sliding friction. This is because fluid friction depends on the object's shape and size,
and the properties of the fluid, while sliding friction is determined by the force pushing the surfaces together and the materials of the surfaces.
Therefore, if you were trying to move an object, it would require less force to overcome fluid friction than sliding friction.
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two pool balls, each moving at 2 m/s, roll toward each other and collide. suppose after bouncing apart, each moves at 2 m/s. assume the positive direction is to the right. this collision violates conservation of a. kinetic energy b. momentum c. both kinetic and momentum d. none of the above
Answer:
(D) From what has been given
For a linear elastic collision the speed of separation equals the speed of approach - if the relative speed of approach was 4 m/s, the relative speed of separation will be 4 m/s - both KE and momentum are considered conserved
There are 2 ways of collecting the sun’s energy. What are they? Give an example of each.
Which is the equivalent of 2000 mm?
a. 200 m b. 2 m c. 0.002 m d. 0.02 m
2000 mm is equivalent to 2 m. This can be derived from the fact that 1 m = 1000 mm. Thus, 2000 mm would be equal to 2 m since it is twice the length of 1000 mm. This conversion is important in various fields such as construction, engineering, and science where precision is necessary.
It is crucial to be able to convert between different units of measurement in order to make accurate calculations and measurements.The millimeter is a unit of length that is often used to measure small distances such as the thickness of a sheet of paper or the size of a small component. It is part of the metric system, which is a system of units used across the world that is based on multiples of 10.
This system makes it easy to convert between different units since it is based on a consistent set of rules.For example, to convert 2000 mm to meters, we can simply divide by 1000 since there are 1000 millimeters in a meter. This gives us 2 meters, which is the equivalent length in meters of 2000 millimeters.
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What is the difference between a psychologist and a psychiatrist?
Answer:
Psychiatrists are medical doctors, psychologists are not. Psychiatrists prescribe medication, psychologists can't. Psychiatrists diagnose illness, manage treatment and provide a range of therapies for complex and serious mental illness. Psychologists focus on providing psychotherapy (talk therapy) to help patients.
Explanation:
Answer:
Psychiatrists are medical doctors, psychologists are not. Psychiatrists prescribe medication, psychologists can't. Psychiatrists diagnose illness, manage treatment and provide a range of therapies for complex and serious mental illness. Psychologists focus on providing psychotherapy (talk therapy) to help patients.
Explanation:
What is the speed of a 55.0 kg skydiver who has 7.81 x 104 J of kinetic energy?
Answer:
v=53.3m/s
Explanation:
Ek=1/2mv²
7.81×10⁴=1/2×55.0v²
v= the square root of 7.81×10⁴/0.5×55.0
v=53.3m/s
The speed of a 55.0 kg skydiver who has 7.81 x 104 J of kinetic energy is 53.29 m/s.
To find the speed, the given values are,
Mass m = 55 Kg
Kinetic Energy = 7.81x 10⁴ J
What is Speed?Speed is the rate of change of distance with time. It is a scalar quantity with magnitude both no direction.
Speed = Distance / Time m/s.
The unit is m/s or km/hr or mile/hr.
Distance covered is simply the length of the path traveled. The unit is m or km or miles.Time taken is the duration of an event. The unit is seconds or minutes or hour.Formula,
Kinetic energy = Ke = 1/2 mv²
When we solve for v,
v² = 2Ke/m
Substituting the given values,
v² = 2(7.81 x 10⁴) / 55
Simplifying,
v² = 15.62 x 10⁴ / 55
v² = 0.284 x 10⁴
v = 0.53291 x 10⁴
v = 53.29 m/s.
The speed of a 55.0 kg skydiver who has 7.81 x 104 J of kinetic energy is 53.29 m/s.
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A batter pops a ball straight up (a) If the ball returns to the height from which it was hit 4.5 s later, what was its
initial speed? (b) Does the ball reach its maximum height 2.25s after it was hit, more than 2.25s after it was hit, or
less than 2.25s after it was hit? Explain. (c) Find the maximum height of the ball, as measured from the point
where it was hit.
Answer:
it depends on how hard and fast he hit the ball a baseballs terminal velocity, a baseball can reach a velocity of around 95mph
Saturn is 890,700,000 miles from the Sun. What is the distance in meters?
Answer:
1.4936 trillion meters
Explanation:
From an average distance of 886 million miles Saturn is 9.5 astronomical units away from the sun
pleaseeee helpp quickkkk
A skateboarder starts at the top of a halfpipe ramp, skates through the middle, and up the other side.
Match the following to describe what is happening at each of the three points in the skater's movement.
Question 1 options:
Middle
End
Beginning
1.
Maximum kinetic energy
2.
Potential and kinetic energy equal
3.
Maximum potential energy
Answer:
Explanation:
1=3
Baker's weight and mass are measured on Earth and on the moon. Which measurement is the same in both places?
Answer: mass
The mass of a person is constant, weight is a force that is influenced by gravity.
5. Gravitational force gets weaker as ________ increases and gets stronger as the __________ of the object increases.
Answer:
Distance, Mass
a factory has a machine which bends wire at a rate of 3 unit(s) of curvature per second. how long does it take to bend a straight wire into a circle of radius 4?
It would take 1/12 seconds to bend a straight wire into a circle of radius 4 using this machine.
The curvature of a circle is defined as the inverse of its radius. So a circle with radius 4 has a curvature of 1/4.
If the machine bends wire at a rate of 3 units of curvature per second, then it would take 1/3 seconds to bend a wire into a circle with curvature of 1.
To bend a straight wire into a circle of radius 4, we need a curvature of 1/4. So the time it takes to bend the wire would be:
(1/4) x (1/3) = 1/12 seconds.
Therefore, it would take 1/12 seconds to bend a straight wire into a circle of radius 4 using this machine.
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how are speed and velocity related? choose all that are true. group of answer choices speed is average velocity speed is the rate of change of velocity speed is the magnitude of velocity velocity is an object's speed and which direction its traveling speed and velocity can be measured in the same units speed and velocity have different units
Speed is the rate of change of distance, while velocity is the rate of change of position. Speed is a scalar quantity, which means it only has magnitude and no direction, while velocity is a vector quantity, which means it has both magnitude and direction. Therefore, all options except the first one are true. Speed can be measured in units such as meters per second (m/s).
Velocity has units of meters per second in a specific direction. This means that velocity is a vector quantity and has direction while speed is a scalar quantity and only has magnitude.
In short, speed is just a scalar representation of velocity, it tells you how fast an object is moving, but it doesn't tell you the direction of motion, whereas velocity tells you both the speed and the direction of motion.
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What is the kinetic energy of a 0.500 kg toy car moving at a state of 1.50 m/s
Answer:0.563
Explanation:
The kinetic energy produced in a toy car is equal to 0.563 J.
What is the kinetic energy and potential energy?The energy exhibited by a moving body because of its motion is said to be its kinetic energy. Work should be done which can change the kinetic energy of a moving object.
The kinetic energy of a moving object can be determined from the formula mentioned below:
K.E. = ½mv² where ‘m’ and ‘v’ is the mass, velocity of the object.
Potential Energy (P.E.)is energy that is stored in an object due to its position and can be expressed as P.E = mgh where h, m, and g are the height, mass, and gravitational acceleration respectively.
Given, the mass of the toy car =, m = 0.500 Kg
The velocity of the toy car, v = 80 m/s
The kinetic energy = (1/2)× 0.500 ×(1.50)²
K.E. = 0.563 J
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The ratio of the speed of light in a vacuum to the speed of light in a given medium isone, since the speed of light is constantthe index of refraction3E+08 meters/secondSnell's Lawtotal internal reflection
le inser is totally!: The ratio of the speed of light in a vacuum to the speed of light in a given medium is NOT one, since the speed of light changes when it passes through a medium with a different refractive index.
The speed of light in a vacuum is approximately 3.00 x 10^8 meters per second, and this value is considered to be a fundamental constant of nature. However, when light passes through a medium such as air, water, or glass, its speed changes depending on the optical properties of the medium. This change in speed is described by the refractive index of the medium, which is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.
Snell's Law describes the relationship between the angles of incidence and refraction for a light ray passing through the boundary between two media with different refractive indices. Total internal reflection occurs when a light ray traveling in a medium with a high refractive index is incident on a boundary with a medium of lower refractive index at an angle greater than the critical angle, causing the ray to be reflected back into the original medium rather than refracted into the second medium.
The ratio of the speed of light in a vacuum to the speed of light in a given medium is known as the index of refraction. This ratio is always equal to one in a vacuum since the speed of light is constant at 3E+08 meters/second.
Snell's Law is used to calculate how light refracts or bends when it passes through different mediums with varying indices of refraction. When the angle of incidence is greater than the critical angle, total internal reflection occurs, causing all of the light to reflect back into the original medium instead of refracting into the second medium.
The index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of light in a given medium. It can be expressed as n = c/v, where n is the index of refraction, c is the speed of light in a vacuum (approximately 3E+08 meters/second), and v is the speed of light in the medium. Snell's Law relates the angles and indices of refraction when light passes from one medium to another. Total internal reflection occurs when the angle of incidence is greater than the critical angle, causing all light to be reflected within the medium.
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