you decide that you want to be able to adjust the width of the views and the data visualizations about electric vehicle sales, charging stations, and battery range. which type of layout will enable you to do that?

The definition of amplitude is that displacement of the particle from the main position is known as the amplitude.

Suppose that there is a spring which has a block connected to one of its end and the other and is connected to a solid rigid wall.

Now let us say that we give a push to the block.

If ignore the air resistance, then we will observe that, the block will show a to and from movement from the initial position of the spring which is in the middle of the to extreme positions of the spring.

The distance that is covered by the block when it most away or towards the spring is known as the amplitude of the spring block system.

This is how we conclude that the displacement of the particle about its mean position is known as amplitude.

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Two balls are dropped from the same height at  1 second interval of time. The separation between the two balls after 2 seconds of the drop of the 1st ball is 14.7 m

For the motion of first ball ,

u = 0

a = g

t₁ = 2 s

∴  The distance travelled by the first ball in 2 s

S₁ = [tex]\frac{1}{2}[/tex] g t₁²

∴  S₁ = [tex]\frac{1}{2}[/tex] × 9.8 × (2)²

∴ S₁ = 4.9 × 4

∴ S₁ = 19.6 m

For the motion of second ball ,

u = 0

a = g

t₂ = 2-1 = 1 s

∴  The distance travelled by the second ball in 1 s

S₂ = [tex]\frac{1}{2}[/tex] g t₂²

∴  S₂ = [tex]\frac{1}{2}[/tex] × 9.8 × (1)²

∴ S₂ = 4.9 × 1

∴ S₂ = 4.9  m

Separation between the two balls = S₁ - S₂

∴ Separation = 19.6 - 4.9

∴ Separation = 14.7 m

The distance separating the balls as time goes on is 14.7 m

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The coefficient of kinetic friction between the mass and the incline is μ is 0.89

The formula for calculating force owing to friction isμ = F/N.

Normal force (N) at an incline is N= mgcosФ, where =32.51

P=F×x is the power corresponding to work done by friction.

The item "spent its energy" and the variable x is displacement.

P= mghcosФ, where h is the height, is the power unit for gravitational force work.

As shown in the illustration, the decrease shapes a triangle with a horizontal plane.

To calculate the frictional force:

MghcosФ = F×x MghcosФ

Changing the force: mghcosФ/x= mgcosФ

μ= h/x

Using trigonometry relations to calculate h

sin(32.51) = h/1

μ = Sin (32.51)/1

μ= 0.89

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The aforementioned Red Giant is the oldest star; the Sun, our own star and largest, is the middle star; and the star on a disc, which is the youngest star, is the last star.

This is how the stars are ranked according to their present ages. In a late stage of stellar evolution, a red giant is a bright giant and oldest star with a low or intermediate mass (about 0.3 to 8 solar masses (M)). Oldest star radius is vast and the surface temperature is roughly 5,000 K (4,700 °C; 8,500 °F) or lower due to the inflated and fragile nature of the outer atmosphere. Is known as red giant.

A hot, incandescent ball of hydrogen and helium at the Centre of our solar system, our Sun is a 4.5 billion year old star. Around 93 million miles separate Earth from the Sun (150 million kilometers).

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Solar activity associated with Space Weather can be divided into four main components: solar flares, coronal mass ejections, high-speed solar wind, and solar energetic particles.

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The gravitational force makes them to attract, and the mass of the small star is 10.87 x 10 ^ 11 kg.

Gravitational force is a force that attracts any two objects with containing mass. It can be said that the gravitational force attractive because it always tries to pull masses together, it never pushes them apart.

Gravitational force is

Fg = Gm1m2/r^2

putting the appropriate values we get

6.7  =  (G x 1018 x m2)/105^2

m2 = (6.7 x 105 x 105)/ 6.67 × 10-11 x1018

m2 = 10.87 x 10 ^ 11 kg

Hence the mass of the second object is 10.87 x 10 ^ 11 kg.

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The work done on a system by a constant force is the component of force in the motion times the displacement through which the force acts.

Work done is said to be 1 J when a force of 1 N is moved through a displacement 1 m along the direction of force.

The formula for work done is given as W = F × s

where, F is the force

s is the displacement

Force can be written as a product of mass and acceleration i.e, F = m × a

where, m is mass

a is acceleration

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The change in decibel will be 3 dB , 6 dB, 9 dB.

What is a decibel?

One-tenth of bel is equivalent to one decibel, which is a relative unit of measurement. It uses a logarithmic scale to express the ratio of two values of a power or root-power quantity. The power ratio of two signals with a one-decibel difference in levels is 101/10, or 10120 for the root-power ratio.

decibel (dB), a unit for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds.

The decibel is a just logarithmic scale

Δβ2 = 10 * log(2) = 3dB

Δβ4 = 10 * log(4) = 6dB

Δβ8 = 10 * log(8) = 9dB

3 dB , 6 dB, 9 dB

Hence, the answer is 3 dB, 6 dB, and 9 dB.

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a) The rotational kinetic energy after the combination rotates through 90° is  7.868 J

(b) The angular speed of the rod and ball is approximately 8.27 rad/s

(c) The linear speed of the rod and ball is approximately 2.35 m/s

(d) The linear speed of the rod and ball combination is 0.01 m/s faster than the speed of ball free falling from 28.4 cm

The Given:

Length of the cylindrical rod, l = 23.4 cm

Mass of the rod, m = 1.20 kg

Mass of ball, M = 2.00 kg

Diameter of the ball, d = 10.00 cm

The rotational kinetic energy of the ball when it rotates 90° :

The total potential energy of the rod and ball at the top is the rotational kinetic energy of the ball at the bottom

 PE( rod)= 0.5 × m× g × l

∴  PE (rod)  = 0.5×1.20×9.81×0.27 = 1.58922

PE (ball) = 2×9.81×(0.27 + 0.05) = 6.2784

 PE (Total) = 1.58922 J + 6.2784 J ≈ 7.868 J.

KE (rot) = 7.868 J.

KE = [tex]\frac{1}{2} \times I \times \omega^2[/tex]

moment of inertia I = moment of inetia of rod + moment of inetia of Ball

I (rod) = [tex]\frac{m . L^2}{3}[/tex] = [tex]\frac{.234^2 \times1.20 }{3}[/tex] =0.0657

I ball =  (⅖ )MR^2 + M (R+L)^2

=[tex]\frac{2}{3} \times 2 \times 0.05^2+2(0.05+0.234)^2[/tex]

=0.0033+0.1613 =0.1646

I = 0.1646 + 0.0657 =0.230 kg·m²

[tex]\frac{1}{2} \times 0.230\times \omega^2[/tex] =7.868

[tex]\omega^{2}[/tex] = 7.868* 2/.230 =68.41

Angular velocity [tex]\omega =\sqrt{68.4}[/tex]

= 8.27 rad per sec

The linear speed, v = ω × r

=8.27*(0.05+.0234) =2.35 m/s

The speed of the ball falling freely from a height of 28.4 cm is given as :

[tex]V^2 = 2gh[/tex]

= 2*9.8*.284= 5.57

v=2.36

The linear speed following the rotation of the combination is approximately 0.01 m/s faster than the speed of the ball in free fall.

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Work done directly proportional to square of length compressed.

Given that the work done W = 180 J

length of compression is d = 0.18 m

The work done by the spring force is

W =(1/2)kd2

k = 2W /d2

=11111.11 N/m

If the length of compression is (0.18 m + 0.18 m)    

then work done

W = (1/2)k(0.36 m)²

= 720 J

= 180 J +  540J

so it is greater than 180J

This is possible because of Work done directly proportional to square of length compressed

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In the radio spectrum, hydrogen atoms emit electromagnetic radiation that can pass through the Milky Way's dust, as was discovered by astronomers.

The office complex was extremely expensive. This month, our phone bill was outrageous. To represent contemporary usage of the word "astronomical," these example sentences were chosen programmatically from various internet news sources.

The two primary categories of astronomy are theoretical and observational. Telescopes and photographers are used in mathematics and astronomy to view or observe constellations, galaxy clusters, and other celestial objects. Observations are explained by theoretical astronomy

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The answer is 97.47 dB.

Solution:

I = 83 dB ; n = 28

we know that

I(dB) = 10 log (I/I0)

83 = 10 log (I/I0)

8.3 = log (I/I0)

I/I0 = 10^8.3

I(combined) = 10 log (28 x 10^8.3) = 97.47 dB

Hence, I(combined) = 97.47 dB

The logarithmic sound intensity scale corresponds to human hearing. Doubling the intensity increases the sound level by 3 dB. The closer or further away the particles are, the greater the amplitude of the sound. Sound amplitude determines the loudness and strength of the sound. The higher the amplitude, the louder and more intense the sound. Sound intensity is measured in watts per square meter.

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A projectile of mass m is fired horizontally from a height h above the level ground and with a speed v. solve for the following in terms of m, h, v, and appropriate constants. The work done by the projectile is 'mgh' and its kinetic energy will be  [tex]\frac{1}{2} m v^{2} cos^{2}[/tex] θ.

Given,

Mass of the projectile = m

The height at which projectile is given 'h'.

Speed of the projectile is 'v'.

As the projectile is fired horizontally, that is the angle θ = 0 degree.

And 'g' is the acceleration due to gravity.

(a) The work done when the applied force and distance or height (h) are in parallel:

W = Fh (cosθ) .....(1)

Where F is the force exerted by the gravity on the projectile

So, F can be written as, F = mg ....(2)

Putting equation (2) in (1).

We get, W = mgh (cosθ)

Where θ = 0 degree

So, W = mgh (cos[tex]0^{0}[/tex])

W = mgh

This is the work done by the gravity on the projectile when the projectile is in horizontal direction.

(b) To determine kinetic energy of the projectile in horizontal:

Velocity component at x axis will be [tex]v_{x}[/tex] =  v cos θ

In general the Kinetic energy of an object moving with mass (m) with a velocity 'v' = [tex]\frac{1}{2}[/tex]m[tex]v^{2}[/tex]

For a projectile it can be written as, K.E = [tex]\frac{1}{2}[/tex] m(v cos θ)^2

Or, K.E = [tex]\frac{1}{2} m v^{2} cos^{2}[/tex]θ

Hence, the work done by the projectile is 'mgh' and its kinetic energy will be  [tex]\frac{1}{2} m v^{2} cos^{2}[/tex] θ.

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23 percent of the sun's energy is directly absorbed by clouds, aerosols, water vapour, and ozone. 25 and 5 percent of the solar radiation that enters the atmosphere from the surface are transferred via evaporation.

Distributed solar power often connects to the regional utility distribution system and can be installed on rooftops or on the ground. The clients of distributed solar are impacted by a wide range of federal, state, and municipal legislation.

You learned in the last module that the tilt, rotation, and revolution of the Earth prevent solar radiation from reaching all part of the planet evenly.

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After an object has travelled a certain distance, the student must calculate the work that is done on it when an external force is applied to it.

An object at location x = 0 experiences an external force F from a string as it traverses a distance D over a horizontal surface for a period of time . As the thing moves, the force changes so that it becomes less.

The final kinetic energy of the object must have been lower than the work performed on it by the applied force, indicating that another external force must have been involved.

Therefore, the learner must determine the work that is done on an object when an external force is applied after it has moved a particular distance.

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The width of the slit will be "  1.27mm".

The single-slit diffraction experiment allows us to examine the phenomena of light bending, or diffraction, which enables coherent light from a source to interfere with itself and generate the diffraction pattern, a recognizable pattern on the screen.

The given values are:

Wavelength = 623 × 10⁻⁹m

Length, L = 3.30 m

we know that,

y/l = m(wavelength)/a

2 × 10⁻³   = 1 (623 × 10⁻⁹)

  3.3                  a

On Cross multiplication, we get,

a = 623 × 10⁻⁹ ×  3.3

          2 × 10⁻³

a = 0.001027m = 1.27mm

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The frequency is 5.9 jules.

we have been given that the mass is equal to 2.4 kgs and the amplitude others 9.3 and returned to the power -2 m. Yeah. So he can write The angular frequency is two pi f. That is To buy into 3.8 Hz. That is equal to 23.87. Ready for a 2nd. Now to find the first concert,

we can write Omega Square. Um that is 23.87 reading perspective, but you didn't one second. We square this into 2.4 gauges. That is equal to 1,36, newtons per meter. How to find the total energy we laid half. Okay, A square that is equal to one by two and 21368.26 into 9.3 to 10 to the minus two squared. That is equality 5.9 Jules.

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Volume of the balloon occupy in the instant before it bursts is 7.39 litres and can be find out by boyle's law.

Boyle’s law:

This law gives the relationship between initial and final pressure and volumes for an ideal gas.

Initial condition

Let the volume of the balloon is V1=2.00 L

And, the initial pressure is P1=1.75 atm

Final condition

Let the volume of balloon before it bursts is V2

final pressure is P2=360 mmHg

                                =360/760 atm

                                =0.7368 atm
                           (1atm=760mmHg)

Now, according to boyle’s law

P1V1=P2V2

V2=P1V1/P2

V2=1.75*2.00/0.47368 L

V2=1.39L

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Using standard heat of formation we can calculate the standard enthalpy Change for this reaction.

What is reaction?

Reaction is a process that's leads to the chemical transformation of one set of chemical substances to another.

Sol-In this question they have us that using standard heats of formation, so here we have to use standard heats of formation, so by using standard heats of formation, we have to calculate standard enthalpy change. So here we have to calculate standard enthalpy change for the particular reaction. So what is the given reaction for that? We have to find out standard, enthalpy change, so the reaction here. It is c that is the solid graphite plus oxygen gas. It gives rise to c to gas. This is the reaction for this reaction. We have to find out standard heat of formation. That is so here we have to. By using standard heat of formation, we have to calculate standard enthalpy change. That is the question, so we know that standard heat of formation of graphite- that is the graphite graphite. That is equal to 0 kilo, joules per mole, so here there's a hitch of formation of oxygen gas, oxygen gas that is equal to 0. So this is the 0 kilo joules per mole and here also delta hedge of formation of oxygen. Gas is equal to 0 kilo, joulesper mole, so delta h of the formation of carbon dioxide gas. So it will be, it is so what it be. It will be. The minus 393.5 kilo joules per mole, so delta h of formation of carbon dioxide gas, is equal to minus 393.5 kilo joules per mole. This is the ans.

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The average intensity of an electromagnetic wave with a peak magnetic field strength of B is I = cB^2/2µo

Define the intensity of an EM wave?

The energy that crosses per second per unit area perpendicular to the electromagnetic wave's direction is what is referred to as the wave's intensity.

Any wave's energy is proportional to its amplitude squared. Thus, the intensity of electromagnetic waves can be written as

I = cε0E^2/2

where

I represents the average intensity of the EM wave in W/m^2.

E represents the strongest possible electric field created by a continuous sinusoidal wave

c  is the speed of light

ε0 is the permitivitty of free space

If B is the strongest possible magnetic field and µo  is the permeability of free space, then the average intensity of an electromagnetic wave, I, can also be represented in terms of the strength of the magnetic field using the relationships

B = E/c, and

ε0 = 1/µo c^2

The highest magnetic field strength B can also be used to express this as,

I = cB^2/2µo

Hence, the average intensity of an electromagnetic wave with a peak magnetic field strength of B is I = cB^2/2µo

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The ball with the greatest ∆v will also have the greatest m×∆v. And if impulse is equal to the momentum change, then the ball with the greatest m×∆v also encounters the greatest impulse.

The critical element is that to change momentum we need to either use more force or growth the period of the identical force. The extra the impulse of force, the extra the trade to momentum of a body projectile, human frame, tennis racket, ball, and so forth.

For a force with a constant importance, we are able to find the importance of the impulse with the aid of multiplying the importance of the pressure by the point that force is exerted. If the pressure is not steady, we simply integrate the pressure characteristic over the set time period.

While one force is extra than every other, the forces are not balanced, they may be unbalanced. Through making use of an unbalanced force, you could change the movement of an item. Unbalanced forces could make an item at relaxation start moving, make a moving item stop, or exchange the course and speed of the item.

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1. phase difference = 45.1318°

2. phase difference = 54.52°

3. phase difference = 62.153°

Case 1: C = 56.4 ₙF

V₁ = [tex]\frac{156}{\sqrt[]{2} }[/tex]

[tex]x_{c}[/tex] = [tex]\frac{1}{2\pi fc}[/tex]

[tex]x_{c}[/tex] = [tex]\frac{1}{2\pi * 60*56.4*10^{-9} }[/tex]

[tex]x_{c}[/tex] = 47.031 KΩ

here, [tex]V_{0} = V_{A}[/tex]

[tex]X_{L}[/tex] = 2πfL

[tex]X_{L}[/tex] = 2π x 60 x 125

[tex]X_{L}[/tex] = 94.247 KΩ

Apply KCV of node "A"

[tex]\frac{V_{A}-0 }{-jX_{c} +jX_{L}+R_{2} }[/tex] + [tex]\frac{V_{A} -V_{1} }{R_{1} }[/tex] = 0

[tex]V_{A}[/tex] ( [tex]\frac{1}{R_{2} +j(X_{L} -X_{C} )} + \frac{1}{R}[/tex] ) = [tex]\frac{V_{1} }{R_{1} }[/tex]

[tex]V_{A}[/tex] ( [tex]\frac{1}{47 + j(94.247 - 47.031)} + \frac{1}{67}[/tex] = [tex]\frac{156/\sqrt[]{2} }{67}[/tex]

[tex]V_{0} = V_{A} = \frac{84.227}{\sqrt{2} }[/tex]

[tex]V_{A}[/tex] = 84.227 sin (2π x 60t + 22.663) Volts

[tex]V_{R} _{1}[/tex] = [tex]V_{1}[/tex] = [tex]V_{A}[/tex] = [tex]\frac{84.706}{\sqrt{2} }[/tex]

V[tex]R_{1}[/tex] = 84.706 sin [2π x 60t + (-22.498°)] Volts

phase difference = 22.6333 - (-22.498)

phase difference = 45.1318°

Case 2: C = 100ₙF

[tex]X_{C}[/tex] = [tex]\frac{1}{2\pi * 60 * 100 * 10^{-9} }[/tex]

[tex]X_{C}[/tex] = 26.525 Ω

[tex]V_{0}[/tex] = [tex]\frac{156}{\sqrt{2} }[/tex] x [tex]\frac{R_{2} + j (X_{L} - X_{C}) }{R_{1} + R_{2} +j(X_{L} - X_{C} )}[/tex]

[tex]V_{0}[/tex] = [tex]\frac{96.98}{\sqrt{2} }[/tex] [tex]\\ 24.52[/tex]° Volts

[tex]V_{R1}[/tex] = [tex]V_{1}[/tex] - [tex]V_{0}[/tex] = [tex]\frac{78.82}{\sqrt{2} }[/tex] -30° Volts

phase difference = 24.52 - (-30)

phase difference = 54.52°

Case 3: C = 500ₙF

[tex]X_{C[/tex] = 5.305 KΩ

[tex]V_{0}[/tex] = [tex]\frac{156}{\sqrt{2} }[/tex] ([tex]\frac{47 + j 94.247 - j 5.305}{67 + j 94.247 - j 5.305 + 47}[/tex])

[tex]V_{0}[/tex] = [tex]\frac{108.533}{\sqrt{2} }[/tex] (24.186°)

[tex]V_{R1} = V_{1} - V_{0}[/tex] = [tex]\frac{72.28}{\sqrt{2} }[/tex] (-37.967°) Volts

phase difference = 24.186 - (-37.967) Volts

phase difference = 62.153°

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The evolutionary value of Five-Factor Model dimension of Neuroticism is that neurotic individuals have greater likelihood of surviving due to the reason that they are overly cautious and attuned to danger.

The Five Factor Model of general personality structure consists of five broad domains of neuroticism that are : extraversion, openness, agreeableness and conscientiousness. These traits reflect the huge differences between people in their motivations.

A broad construct conveying a predisposition to experience psychological distress and negative mood states is called neuroticism. Component subscales of neuroticism are: personality traits of anxiety, hostility, depression, social anxiety, impulsiveness and vulnerability to stress.

Neuroticism is defined as a broad personality trait dimension representing the degree to which a person experiences the world as distressing, threatening and unsafe.

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The horizontal acceleration of the softball after she lets go of the ball is  0 m/s².

option B is the correct answer

During a projectile motion, the vertical acceleration of a projectile decreases as the projectile moves upwards and eventually become zero as the object reaches the maximum height.

As the object begins move downwards, the vertical velocity of the projectile increases and eventually becomes maximum before the object hits the ground.

During the horizontal motion of a projectile, the horizontal velocity of the projectile does not change. That is the initial horizontal velocity of the projectile equals the final horizontal velocity of the projectile.

a = v - u/t

where;

Since, final horizontal velocity = initial horizontal velocity

v = u

a = 0

In summary, the vertical velocity of the a projectile changes while the horizontal velocity does not change. This results in a zero horizontal acceleration of the projectile.

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Newton's law of gravitation says that the magnitude f of the force exerted by a body of mass m on a body of mass m is f = Gmm/r².

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

The gravitational constant, denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.

f = Gmm/r²

Newton's law of gravitation says that the magnitude f of the force exerted by a body of mass m on a body of mass m is f = Gmm/r² where G is the gravitational constant and r is the distance between the bodies.

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According to the statement makes it possible to treat reflected light from a mirror.

The verbs cogitate, deliberate, reason, conjecture, and think are some frequent synonyms for reflect. All of these phrases refer to "using one's faculties of conceptualization, judgment, or inference," but reflect denotes thoughtful reflection on a memory.

unchanging verb. When you reflect, you give something serious thought. We should all allow ourselves space to think. Alternatives: think, evaluate, deliberate, and think. More words for reflect recognizing a people's verbal and nonverbal cues for their feelings and emotions, then expressing (or reflection) those sentiments directly to the user or customer, is known as reflecting feelings.

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2,042.1 years time from now will we see it disappear.

d = 6.44. 3.10¹⁸ m,

v = 3.10⁸ m/s,

t = 6.44.3. 10¹⁸ / 3. 10⁸ s = 6.44 . 10¹⁰ sec.

Converting seconds to years:

6.44. 10¹⁰ sec . (1min/60 sec).(1h/60 min). (1d/24h)(1y/365d) = 2,042.1 years.

Physicists define time as the progression of events from the past through the present, and into the future. If a system doesn't change, it is effectively timeless. When describing events that take place in three-dimensional space, time may be seen as the fourth dimension of reality. We are unable to see, touch, or taste time, yet we can compute how much time has passed.

Everywhere in classical mechanics, time is constant. The timekeeping systems are still in sync. But as Einstein's special and general theories of relativity show, time is relative. It depends on the observer's perspective of view. The theory of time dilation states that when one approaches the speed of light, the intervals between events grow longer (dilates).

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The electric field strength (in v/m) between the plates is 9.117647 X10⁵ eV/m

The electric

field strength can be calculate as follows:

The magnitude of the electric field between two parallel conducting plates is defined as:

E = ΔV

      d

where  ΔV is the potential difference between the plates and d is their separation.

Potential energy is defined as the product of the particle charge and the potential difference.

u = q ΔV

Solve ΔV and subtitute to the electric field equation:

ΔV= U/ q

E= U/qd

In this case we have a double charged ion, so q= 2e

E =    31 x10³ eV     = 911,764.7 eV/m =9.117647 X10⁵ eV/m

    (2e) (1.7 x10⁻²m)

therefore, the electric field strength (in v/m) between the plates is 9.117647 X10⁵ eV/m

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Answer:

s=ut+12at2. S=1m???

Explanation:

initial velocity in vertical direction, is 0m/s ... Hence distance along the floor from the table is 2×0.45=0.9m.

The corresponding gain is 7.81×10-³

With compensation G(s) = k / (s+3) (s+1)

a) closed loop characteristic equation is

1 + G(s) = 0

(s+3) (s+1) + k = 0

s² + 4s + k + 3 = 0 ------ (1)

standard form of characteristic equation is

s² + 2ξ ωn + ωn² = 0 ------ (2)

Given ξ = 1/√2

comparing equation (1) and (2)

ωn² = k+3 , ωn = √(k+3)

2 ξ ωn = 4

2 × 1/√2 × √ (k+3) = 4

√(k+3) = 2√2

k + 3 = 8, k = 5

b) closed loop tranfer function

T(s) = G(s) / 1+G(s)

= 5/ s²+4s+8

magnitude |G(s)| = 5/√ [ (64-ω²)² + (4ω)²]

For maximum gain, denominator --> maximum

d/dω [ (64-ω²)² + 16ω²] = 0

2(64-ω²)² (-2ω) + 32ω = 0

4ω ( -4096 - ω⁴+128ω²+8 ) = 0

ω⁴ + 128ω² - 4088 = 0

ω = 26.6 rad/s

Gn = 5/√ [ (64-ω²)² + (4ω)²]

Gain = 7.81×10-³

learn more damping ratio at

https://brainly.com/question/29490032

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