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Romashka-Z-Leto [24]
3 years ago
7

All of these ODEs model a system with a spring, mass and dashpot.

Mathematics
1 answer:
Wewaii [24]3 years ago
6 0

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

This differential equation will have a characteristic equation of the form:

a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

  • If the discriminant is greater than zero, the solution is over-damped

  • If the discriminant is less than zero, the solution is under-damped

  • If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

-3y''-3y+3y=0

Which has characteristic equation of the form:

-3r^2-3r+3=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-3\\b=-3\\c=3

So:

Disc=(-3)^2-4(-3)(3)=9-(-36)=45

In this case:

Disc=45>0

Therefore the solution is over-damped.

Now, given the differential equation:

-2y''-4y'+1y=0

Which has characteristic equation of the form:

-2r^2-4r+1=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-2\\b=-4\\c=1

So:

Disc=(-4)^2-4(-2)(1)=16+8=24

In this case:

Disc=24>0

Therefore the solution is over-damped.

Finally, given the differential equation:

1y''+7y'+5y=0

Which has characteristic equation of the form:

1r^2+7r+5=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=1\\b=7\\c=5

So:

Disc=(7)^2-4(1)(5)=49-20=29

In this case:

Disc=29>0

Therefore the solution is over-damped.

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Answer:

YES

Step-by-step explanation:

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\frac{1}{4} \\×\frac{5}{5}=\frac{5}{20} (5:20)

Hope this helps!

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2 years ago
What is 6X squared +17 X +13+4 over X -1 multiplied by X minus one
Free_Kalibri [48]

Answer:

6x^{3} + 11^{2} - 4x -9

Step-by-step explanation:

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8 0
3 years ago
James is running on a trail that is 5/4 of a mile long. So far he has run 2/3 of the trail. How many miles has he run so far?
aalyn [17]
Step 1) You would need to convert your 2 fractions into equivalent numbers. In this case, the closet gcf (greatest common factor) is 12. So, 5/4 would convert to 15/12 and  2/3 converts to 8/12.

Step 2) You know have your decimals that are equivalent. All you have left now is to subtract. Take 15/12 and subtract 8/12 from it. You would now get 7/12 of a mile that is still needed to run. 

Step 3) Usually, you would simplify your new fraction. In this case, our fraction doesn't simplify. It will stay 7/12 of a mile. For example, If our number had ended up being 4/12, then we would simplify it to 1/3 of a mile. Because, 4 divided by 4 is 1 and 12 divided by 4 is 3. You can't simplify your answer anymore.

Hope this helped!
3 0
3 years ago
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Joe got a bonus of $1,600.20 based on a certain percent of his sales for the year, which was $22,860. What percent of his sales
lbvjy [14]
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5 0
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Rzqust [24]

The linear function that models the total cost for x deliveries is:

y(x) = 2x + 9

-------------------

A linear function has the following format:

y = mx + b

In which

  • m is the slope, that is, the rate of change.
  • b is the y-intercept, that is, the value of y when x = 0.

In this problem:

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  • Cost of $2 for each delivery, thus m = 2.

The function for the <u>total cost for x deliveries is:</u>

y(x) = 2x + 9

A similar problem is given at brainly.com/question/16270359

4 0
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