How does changing the amplitude affect the wave speed

The solution to the initial value problem that models the given LRC circuit is:

q(t) = e^(-3t/8) * (- (√(3900) / 60)*cos((√(3900) / 80)t) + (3/16)*sin((√(3900) / 80)t))

The initial value problem that models the given LRC circuit can be formulated using Kirchhoff's laws. Let's begin by writing the differential equation representing the circuit:

Lq''(t) + Rq'(t) + q(t)/C = E

where:

L = 40 henrys (inductance)

R = 30 ohms (resistance)

C = 1/300 farads (capacitance)

E = 200 volts (voltage)

q(t) represents the charge on the capacitor at time t.

Now, let's solve this initial value problem.

To solve the differential equation, we need to find q(t).

First, let's find the general solution of the homogeneous equation:

Lq''(t) + Rq'(t) + q(t)/C = 0

The characteristic equation corresponding to this homogeneous equation is:

Lr²+ Rr + 1/C = 0

Substituting the given values, we have:

40r²+ 30r + (1/(1/300)) = 0

40r² + 30r + 300 = 0

Now we can solve this quadratic equation to find the roots (values of r):

r = (-b ± √(b² - 4ac)) / (2a)

Using the quadratic formula, we have:

r = (-30 ± √(30² - 4*40*300)) / (2*40)

r = (-30 ± √(900 - 4800)) / 80

r = (-30 ± √(-3900)) / 80

Since the discriminant is negative, √(-3900) is an imaginary number. Therefore, we have complex roots:

r = (-30 ± √(3900)i) / 80

Let's denote the real part of the roots as α and the imaginary part as β:

α = -30 / 80 = -3/8

β = √(3900) / 80

Therefore, the general solution for the homogeneous equation is:

q(t) = e^(αt) * (c1*cos(βt) + c2*sin(βt))

Now, let's find the particular solution. We are given the initial conditions:

q(0) = 9 (coulombs)

q'(0) = 1 (coulombs/second)

We can use these initial conditions to find the specific values of c1 and c2. Taking the derivative of the general solution, we have:

q'(t) = α*e^(αt) * (c1*cos(βt) + c2*sin(βt)) - e^(αt) * (c1*β*sin(βt) - c2*β*cos(βt))

Substituting t = 0, we get:

1 = α*c1 - c2*β

Differentiating again, we have:

q''(t) = α^2*e^(αt) * (c1*cos(βt) + c2*sin(βt)) - 2*α*e^(αt) * (c1*β*sin(βt) - c2*β*cos(βt)) - e^(αt) * (c1*β^2*cos(βt) + c2*β^2*sin(βt))

Substituting t = 0, we get:

0 = α^2*c1 - 2*α*c2*β - c1*β^2

Using the given values, α = -3/8 and β = √(3900) /

80, we can solve these two equations simultaneously to find c1 and c2.

-3/8*c1 - c2*(√(3900) / 80) = 1/8 (from the first equation)

9/64*c1 - (√(3900) / 64)*c2 = 0 (from the second equation)

Solving these equations, we find:

c1 = - (√(3900) / 60)

c2 = 3/16

Therefore, the particular solution is:

q(t) = e^(-3t/8) * (- (√(3900) / 60)*cos((√(3900) / 80)t) + (3/16)*sin((√(3900) / 80)t))

Thus, the solution to the initial value problem that models the given LRC circuit is:

q(t) = e^(-3t/8) * (- (√(3900) / 60)*cos((√(3900) / 80)t) + (3/16)*sin((√(3900) / 80)t))

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Answer:

the second law of thermodynamics. that some energy is destroyed in every energy conversion.

Explanation:

According to the second law of thermodynamics, energy conversion is never 100% efficient. Some energy is always lost as it is being converted from one form to the other.

The fact that a steer must eat at least 100 pounds of grain to gain less than 10 pounds of muscle tissue shows that not all the energy taken up from the grain is channelled towards building the muscle tissue. Some energy from the grains are lost on the way according to the second law of thermodynamics.

Answer:

b. an electric current is used to turn the pointer of a galvanometer

Explanation:

well , galvanometer is an important device which is used to detect an electric current through a conductor or circuit.

something special about it is that it can detect very minute current too

Answer:

b

Explanation:

The position of the image relative to the mirror v = 20cm, position of the image behind the mirror.

Since object is always placed in front of the mirror

Hence, object distance will be negative

Object distance (u) = - 100cm

Focus of a convex mirror is behind the mirror

Hence focal length will be positive

Focal length (f)= + 25cm

Find position of the image

Let the image distance = v

Using formula,

\(\frac{1}{v}\) +\(\frac{1}{u}\) = \(\frac{1}{f}\)

\(\frac{1}{v}\) = \(\frac{1}{f} - \frac{1}{u}\)

\(\frac{1}{v} = \frac{1}{25} - \frac{1}{-100}\)

\(\frac{1}{v} = \frac{1}{25} + \frac{1}{100}\)

\(\frac{1}{v} = \frac{4 + 1}{100}\)

\(\frac{1}{v} = \frac{5}{100}\)

v = \(\frac{100}{5}\)

v = 20cm

Since v is positive

Hence, image is 20cm behind the mirror

Nature of image is Virtual and erect.

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Answer:

As the temperature increases, the kinetic energy of the molecules of the liquid increases.

Explanation:

Answer: 4 times grease

Explanation: Force F= C · q1·q2/r². C = Coulomb's constant.

If charges double you have 2q1 and 2q2.

Answer:

1. v₂ = 12.43 m/s

2. I₁ = - 80 N.s

3. I₂ = 80 N.s

Explanation:

Consider the following data given in the question:

m₁ = mass of the Cart 1 = 16 kg

m₂ = mass of the Cart 2 = 7 kg

u₁ = velocity of cart 1 before collision = 4 m/s

u₂ = velocity of cart 2 before collision = 1 m/s

v₁ = velocity of cart 1 after collision = - 1 m/s

v₂ = velocity of cart 2 after collision = ?

1.

Applying the law of conservation of momentum:

\(m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}\\(16\ kg)(4\ m/s)+(7\ kg)(1\ m/s)=(16\ kg)(-1\ m/s)+(7\ kg)(v_{2})\\v_{2} = \frac{87\ kg.m/s}{7\ kg}\)

v₂ = 12.43 m/s

2.

Impulse of cart 1 = I₁ = m₁(v₁ - u₁)

I₁ = (16 kg)(- 1 m/s - 4 m/s)

I₁ = - 80 N.s

3.

Impulse of cart 2 = I₂ = m₂(v₂ - u₂)

I₂ = (7 kg)(12.43 m/s - 1 m/s)

I₂ = 80 N.s

The wavelength of the scattered light is approximately 2.468 × 10^-12 m. When light of wavelength 4.89 pm is scattered at an angle of 94.6° from the incident direction by free electrons in a target.

We need to calculate the wavelength of the scattered light.

The electron Compton wavelength is given as 2.43 × 10^-12 m.

The scattering of light by free electrons can be described using the concept of Compton scattering. According to Compton's law, the change in wavelength (Δλ) of the scattered light is related to the initial wavelength (λ) and the scattering angle (θ) by the equation:

Δλ = λ' - λ = λc(1 - cos(θ))

where λ' is the wavelength of the scattered light, λc is the electron Compton wavelength, and θ is the scattering angle.

Given that λ = 4.89 pm = 4.89 × 10^-12 m and θ = 94.6°, we can plug these values into the equation to find the change in wavelength:

Δλ = λc(1 - cos(θ)) = (2.43 × 10^-12 m)(1 - cos(94.6°))

Calculating the value inside the parentheses:

1 - cos(94.6°) ≈ 1 - (-0.01435) ≈ 1.01435

Substituting this value into the equation:

Δλ ≈ (2.43 × 10^-12 m)(1.01435) ≈ 2.468×10^-12 m

Therefore, the wavelength of the scattered light is approximately 2.468 × 10^-12 m.

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Answer:

The acceleration of proton is 5.56 x 10^10 m/s^2 .

Explanation:

initial velocity, u = 0

Electric field, E = 580 N/C

final speed, v = 10^6 m/s

(a) Let the acceleration is a.

According to the Newton's second law

F = m a = q E

where, q is the charge of proton and m is the mass.

\(a= \frac{q E}{m}\\\\a = \frac{1.6\times10^{-19}\times 580}{1.67\times 10^{-27}}\\\\a= 5.56\times 10^{10} m/s^2\)

Science does not  work when every one does the same thing, some creative thinking will be major breakthroughs for an invention. Therefore, option B is correct.

So how do researchers come up with those particular questions to look into ! It may come as a shock to learn how much imagination is required for the procedure.

Peter Medawar, a Nobel Prize-winning biologist, once described scientific inquiry as "the art of the soluble"  In order to succeed in science, one must first identify the questions that may be answered by scientific study and then determine the answers to those questions, according to Medawar.

Because of how intricate the natural world is, it is frequently impossible to directly address the really intriguing, significant scientific topics

The art of science includes repeatedly re-imagining these complex issues, mentally dividing them into more manageable components, and then guessing as to which of these more manageable components might hold the answer to solving the larger issue.

Therefore, all the discoveries and inventions are resulted from the creative ideas and thoughts of scientists. Therefore, creativity is the only way to make a controlled experiment.

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An international language for communication, aid in organising and comprehending biodiversity, facilitation of research and recording, support for conservation efforts, addition to our understanding of evolution, and consideration of cultural variation are all provided by a system for naming and identifying organisms.

Having a system for identifying and naming organisms is important for several reasons:

Clear Communication: A standardized system of identification and naming allows scientists, researchers, and individuals to communicate clearly and effectively about specific organisms. It provides a common language and reference point, enabling accurate and unambiguous communication about a particular species.

Organization and Classification: The system of identification and naming helps in organizing and classifying the vast diversity of organisms. By assigning unique names to each species, scientists can categorize and group organisms based on their similarities and relationships, making it easier to study and understand the natural world.

Reference and Documentation: The naming system serves as a reference for documenting and recording information about different species. It allows researchers to maintain detailed records of their findings, observations, and studies, facilitating future research, collaboration, and the sharing of knowledge.

Species Conservation and Management: Accurate identification and naming of organisms are crucial for conservation efforts. It helps in identifying endangered or threatened species, monitoring population trends, and implementing appropriate conservation strategies. It also aids in tracking invasive species and managing ecosystems effectively.

Historical and Evolutionary Understanding: The system of naming organisms often reflects their evolutionary history and relationships. By examining the scientific names and taxonomic classifications, researchers can gain insights into the evolutionary patterns, shared ancestry, and evolutionary relationships among different species.

Cultural and Traditional Importance: Many organisms have local, traditional, or cultural names that hold significance in specific regions or communities. Having a standardized system allows for the integration of local names with scientific names, fostering cultural preservation and respecting indigenous knowledge and practices.

Therefore, a system for identifying and naming organisms provides a universal language for communication, aids in organizing and understanding biodiversity, facilitates research and documentation, supports conservation efforts, contributes to our understanding of evolution, and respects cultural diversity.

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Answer:

Positively charged objects attract negatively charged objects.

Explanation:

This is due to a law that states 'like forces attract while unlike forces repel. This same concept applies to magnetism. If you put two similar poles together, for example; if you place two south poles together. You feel a separating force between the two poles. But if you place two opposite poles together they attract each other. Hope i helped.

Answer:

Positively charged objects attract negatively charged objects.

Explanation:

hope this helps

The time interval is 0.15 s

The frequency of oscillation refers to the number of cycles of a periodic waveform that occur per unit of time, usually measured in hertz (Hz), which represents cycles per second.

Based on the information that can get in the question that has been put before us here and now;

Note that;

Frequency = Number of oscillations/Time

3 * 10^3 = 440/time

Time = 440/3 * 10^3

Time = 0.15 s

Thus we can see from the calculation that the time that is taken is 0.15 s

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The image shows the correct way of lining up vectors to add them together, that the two arrows lined up one after the other, therefore the correct answer is option B.

The quantities that contain the magnitude of the quantities along with the direction are known as the vector quantities.

Examples of vector quantities are displacement, velocity acceleration, force, etc.

Thus, the image shows the correct way of lining up vectors to add them together, that the two arrows lined up one after the other, therefore the correct answer is option B.

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When a permanent magnet is placed on top of a straight wire, a magnetic field is produced in the region surrounding the wire due to the motion of charges in the wire. The magnetic field produced by the wire interacts with the magnetic field of the permanent magnet and causes a force to be exerted on the wire.

The direction of the force is perpendicular to both the magnetic field and the current in the wire. If the wire is not fixed in place, it will experience a force and move in a direction that is perpendicular to both the magnetic field and the current in the wire. This phenomenon is known as the Lorentz force, which is the force that is exerted on a charged particle when it moves in an electromagnetic field.

The direction of the force is given by the right-hand rule, which states that if the thumb of the right hand points in the direction of the current, and the fingers point in the direction of the magnetic field, then the palm of the hand will point in the direction of the force. The magnitude of the force is proportional to the current in the wire and the strength of the magnetic field.

Therefore, the stronger the magnetic field or the current, the greater the force that is exerted on the wire. The Lorentz force is the basis for the operation of many devices such as motors, generators, and transformers.

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The wind velocity that will tip the truck over to its side is approximately 45.6 m/s. This is calculated by considering the torque exerted by the wind on the truck's side surface and comparing it to the torque due to the weight of the truck.

To determine the wind velocity that will tip the truck over, we need to calculate the critical wind speed at which the torque exerted by the wind on the truck's side surface overcomes the torque due to the weight of the truck.

The torque due to the wind can be calculated using the equation:

Torque (wind) = (1/2) * air density * velocity² * projected area * moment arm

The torque due to the weight of the truck can be calculated using the equation:

Torque (weight) = weight * moment arm

For tipping to occur, the torque due to the wind must exceed the torque due to the weight of the truck. Therefore, we set the two torques equal to each other and solve for the wind velocity.

(1/2) * air density * velocity² * projected area * moment arm = weight * moment arm

Simplifying the equation, we find:

velocity² = (2 * weight * moment arm) / (air density * projected area)

Substituting the given values:

weight = 5000 kg

moment arm = 0.75 m

air density = 1.1 kg/m³

projected area = length * height = 9 m * 2.5 m = 22.5 m²

We can now calculate the wind velocity:

velocity²  = (2 * 5000 kg * 0.75 m) / (1.1 kg/m³ * 22.5 m²)

velocity² = 204.55

velocity ≈ √204.55 ≈ 14.3 m/s

Therefore, the wind velocity that will tip the truck over to its side is approximately 14.3 m/s.

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Answer:

Pluto

Explanation:

Pluto is now classified as a dwarf planet It used to be a formal planet but not anymore.

Answer:

Measurement is the competion of known quantity to unknown quantity.

Explanation:

I hope that it will be right answer

Answer:

Measurement standard is relationship of a physical quantity.

Explanation:

Measurement standard is the fundamental reference and measuring the compared the device, these reference is controlled to the objects conditions to the physical quantity.

#1

True

All metals attract magnets

#2

Yes true

Away from magnetic field if you place something it won't attract that

#3

False

Its only possible in case of electromagnetic force fields .

#4

False

Electromagnetic force field

#5

True

The cosine rule is used to determine the values of unknown aides and angles in a triangle

The measure of θ is approximately 117.2°

Reason:

Given parameters are;

The distance between the two windmills, a = 456 feet

The distance between the cow and one of the windmills, b = 320 feet

Distance between the cow and the other windmills, c = 210 feet

Required, the angle θ between b, and c direction

Solution;

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(θ)

Which gives;

\(cos (\theta) = \dfrac{320^2 + 210^2 - 456^2}{2 \times 320 \times 210 }\)

The measure of θ ≈ 117.2°

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Answer:it’s c SrBr2

Explanation:

Answer above is correct

Explanation:

In ohms, the resistance of the unknown resistor is 6.19 amps.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Therefore in ohm's law, V = IR

V = voltage

I = current

R = resistance

To calculate the resistance, we have

R = V/I

where Voltage = 29.7

Current , I = 4.8

Resistance= 29.7/ 4.8 = 6.19 amps

In conclusion, Ohm's Law is a formula used to calculate the relationship between voltage, current and resistance in an electrical circuit.

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Three capacitors with capacitance values of 8.0 μf, 11 μf, and 16 μf are connected in parallel. The equivalent capacitance is calculated by adding up the individual capacitances, resulting in a total of 35 μf.

When capacitors are connected in parallel, the equivalent capacitance is equal to the sum of individual capacitances. Therefore, to find the equivalent capacitance of the given capacitors, we simply add their capacitance values.

C_eq = C_1 + C_2 + C_3

C_eq = 8.0 μF + 11 μF + 16 μF

C_eq = 35 μF

The equivalent capacitance of the three capacitors connected in parallel is 35 μF.

In parallel connection, the positive plate of all capacitors is connected together and the negative plate of all capacitors is also connected together. When capacitors are connected in parallel, the voltage across each capacitor is the same and equal to the voltage across the entire circuit. The total capacitance of the circuit is increased, which results in an increase in the amount of charge that can be stored in the circuit.

In practical applications, capacitors are often connected in parallel to increase the capacitance of a circuit. For example, in an audio system, capacitors are used to filter out unwanted noise from the signal. By connecting multiple capacitors in parallel, the amount of noise that can be filtered out is increased, resulting in a cleaner audio signal.

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The equivalent resistance for the parallel connected resistance will be

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω)

Now if two resistances are connected parallel then the voltage on the resistances will be different and the same current will flow from both resistances.

\(V_{eq}=V_1+V_2\)

\(I_{eq}R_{eq}=I_1R_1+I_2R_2\)

Since \(I_{eq}=I_1=I_2\)

\(R_{eq}=R_1+R_2\)

Hence the equivalent resistance for the parallel connected resistance will be

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)

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Alpha particles are the least penetrating and can be shielded with thin materials. Beta particles are intermediate and require thicker shielding. Gamma rays are the most penetrating and need dense shielding

The three types of radiation are alpha particles, beta particles, and gamma rays.

For alpha particles, the most effective shielding is usually a thin sheet of material such as paper, clothing, or even human skin. Alpha particles have a relatively large mass and a positive charge, which means they interact strongly with matter and are easily stopped by even thin materials.

For beta particles, the most effective shielding is usually a slightly thicker material, such as aluminum or plastic. Beta particles are smaller and faster than alpha particles, but still have a charge and can be stopped by moderate amounts of shielding.

For gamma rays, which are a type of electromagnetic radiation, the most effective shielding is usually a dense material such as lead or concrete. Gamma rays have no charge and interact weakly with matter, so they require denser materials to effectively absorb and scatter the radiation.

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Answer:

a) Fnet = 176.78N

b) Enet = 88.39 × 10⁵N/C

Explanation:

Answer:

Friction is another force that energy gets "wasted" on in the dragging. Therefore, the machine gives you less mechanical advantage when too much friction is involved because it wastes energy. It also makes it less efficient!