1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zhenek [66]
3 years ago
5

Consider the differential equation

Physics
1 answer:
Zielflug [23.3K]3 years ago
3 0
Yp(t) = A1 t^2 + A0 t + B0 t e(4t)

=> y ' = 2A1t + A0 + B0 [e^(4t) +4 te^(4t) ]

     y ' = 2A1t + A0 + B0e^(4t) + 4B0 te^(4t)

=> y '' = 2A1 + 4B0e(4t) + 4B0 [ e^(4t) + 4te^(4t)

     y '' = 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t)

Now substitute the values of y ' and y '' in the differential equation:

 
<span>y′′+αy′+βy=t+e^(4t)


</span> 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t) + α{2A1t + A0 + B0e^(4t) + 4B0 te^(4t) } + β{A1 t^2 + A0 t + B0 t e(4t)} = t + e^(4t)

Next, we equate coefficients

1) Constant terms of the left side = constant terms of the right side:

2A1+ 2αA0 = 0 ..... eq (1)

2) Coefficients of e^(4t) on both sides

8B0 + αB0 = 1 => B0 (8 + α) = 1 .... eq (2)

3) Coefficients on t

2αA1 + βA0 = 1 .... eq (3)


4) Coefficients on t^2

βA1 = 0 ....eq (4)

given that A1 ≠ 0 => β =0

5) terms on te^(4t)

16B0 + 4αB0 + βB0 = 0 => B0 (16 + 4α + β) = 0 ... eq (5)

Given that B0 ≠ 0 => 16 + 4α + β = 0

Use the value of β = 0 found previously

16 + 4α = 0 => α = - 16 / 4 = - 4.

Answer: α = - 4 and β = 0
  




You might be interested in
At which temperature does the motion of atoms and molecules stop?<br> 0°C<br> 0C<br> 0°K<br> 0K
anastassius [24]

Answer: 0K

Explanation:

Absolute 0 (0K) is the point where nothing could be colder and no heat energy remains in a substance.

7 0
3 years ago
Explain how the thermal energy of a swimming pool compares to the thermal energy of a lake at the same temperature.
astra-53 [7]
There is more thermal energy in the lake because there is more water which is more thermal energy
3 0
3 years ago
Block B (of mass m) is initially at rest. Block A (of mass 3m) travels toward B with an initial speed v0 (vee nought) and collid
NeTakaya

Answer:

The maximum height reached by the two blocks is approximately 0.1147959 × v₀²

Explanation:

The mass of block B = m

The mass of block A = 3·m

The initial velocity of block B, v₂ = 0 m/s

The initial velocity of block A, v₁ = v₀

The amount of friction between the blocks and the surface = Negligible friction

By the Law of conservation of linear momentum, we have;

Total initial momentum = Total final momentum

3·m·v₁ + m·v₂ = (3·m + m)·v₃ = 4·m·v₃

Plugging in the values for the velocities gives;

3·m × v₀ + m × 0 = (3·m + m)·v₃ = 4·m·v₃

∴ 3·m × v₀ =  4·m·v₃

\therefore v_3 = \dfrac{3}{4} \times v_0 = 0.75 \times v_0

The kinetic energy, K.E. of the combined blocks after the collision is given as follows;

K.E. = 1/2 × mass × v²

\therefore K.E. = \dfrac{1}{2} \times 4\cdot m \times \left (\dfrac{3}{4} \cdot v_0 \right )^2 = \dfrac{9}{8} \cdot m\cdot v_0^2

The potential energy, P.E., gained by the two blocks at maximum height = The kinetic energy, K.E., of the two blocks before moving vertically upwards

The potential energy, P.E. = m·g·h

Where;

m = The mass of the object at the given height

g = The acceleration due to gravity

h = The height at which the object of mass, 'm', is located

Therefore, for h = The maximum height reached by the two blocks, we have;

P.E. = K.E.

m \cdot g \cdot h =  \dfrac{9}{8} \cdot m\cdot v_0^2

h = \dfrac{\dfrac{9}{8} \cdot m\cdot v_0^2}{m \cdot g }  = \dfrac{9}{8} \cdot \dfrac{ v_0^2}{ g }  =  \dfrac{9}{8} \cdot \dfrac{ v_0^2}{ 9.8} = \dfrac{42}{392} \cdot  v_0^2 \approx 0.1147959   \cdot  v_0^2

The maximum height reached by the two blocks, h ≈ 0.1147959·v₀².

7 0
2 years ago
What is Gravitational force?​
mote1985 [20]

Answer:

the force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface

Explanation:

7 0
3 years ago
Read 2 more answers
A circular coil of five turns and a diameter of 30.0 cm is oriented in a vertical plane with its axis perpendicular to the horiz
____ [38]

The horizontal component of the magnetic field is 12.6 μT.

The magnetic influence on moving electric currents, electric charges, and magnetic materials is described by a magnetic field, which is a vector field. When a charge moves through a magnetic field, a force that is perpendicular to both its own velocity and the magnetic field operates on it.

The horizontal component of the Earth's magnetic field is perpendicular to the axis of a circular coil with five turns and a diameter of D = 30.0 cm that is vertically orientated.

A coil current of I = 0.600 A causes a horizontal compass to deflect 45.0° from magnetic north when it is positioned in the coil's center.

Let B be the magnetic field and R be the radius of the circular coil.

Then the horizontal component of the Earth's magnetic field is given as:

B(h) = B(coil) = μ₀ NI / 2R

B(h) = (4π × 10⁻⁷ ) (5)(0.6) / 0.3

B(h) = 12.6 μT

Learn more about magnetic field here:

brainly.com/question/14411049

#SPJ4

5 0
2 years ago
Other questions:
  • What crop is least likely to do well when the temperatures are very hot?
    7·1 answer
  • In order for work to be done, what three things are necessary?
    14·2 answers
  • Which combination of characteristics produces the LEAST energetic waves?
    9·1 answer
  • Aristotle said that a moving earthly or `mundane' object with nothing pushing or pulling on it will always A slow down and stop.
    8·1 answer
  • In a football game, a 90 kg receiver leaps straight up in the air to catch the 0.42 kg ball the quarterback threw to him at a vi
    14·1 answer
  • What is the type of relationship between the height (H) and the atmospheric density, and which segment can give the most accurat
    6·1 answer
  • A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a light b
    10·1 answer
  • I will mark brainliest!! The Moon travels around the Earth each month in an elliptical path, as opposed to a perfect circle.
    13·1 answer
  • A shopper walks westward 2.8 meters in the first 5 minutes and then eastward 9.2 meters in the next 10 minutes. What is the shop
    12·1 answer
  • Cavity wall insulation costs £240 but will save you £32 each year. What is the payback time for cavity
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!