To determine the number of roots of P(s) in the right half-plane, left half-plane, and on the jω-axis, we can use the Routh-Hurwitz stability criterion.
First, we construct the Routh array:
| 1 | 5 | 8 |
| 6 | 5 | 0 |
| -5.6 | 8 |
The first column of the Routh array has all positive elements, indicating that all the roots of the polynomial have positive real parts or are located on the jω-axis. However, the second column has one negative element, indicating that there is one root in the left half-plane.
To determine the number of roots on the jω-axis, we look for the number of sign changes in the first column of the Routh array. In this case, there is one sign change, indicating that there is one root on the jω-axis.
Therefore, the number of roots in the right half-plane is 0, the number of roots in the left half-plane is 1, and the number of roots on the jω-axis is 1.
The Routh array is a tabular method used in control engineering to determine the stability of a linear time-invariant system. It was introduced by Edward John Routh in the 19th century and is a valuable tool in analyzing the roots of a polynomial equation.
To construct a Routh array, the coefficients of the polynomial equation are arranged in a table, starting from the highest order term down to the constant term. The first two rows of the table are then calculated using the coefficients in the polynomial equation as follows:
The first row consists of the coefficients of the even powers of the polynomial.The second row consists of the coefficients of the odd powers of the polynomial.Visit here to learn more about Routh array brainly.com/question/31318894
#SPJ11
The figure is made up of a rectangle, 2 right triangles and a 3rd triangle.
What is the area of the figure?
Responses
34 in2
52 in2
46 in2
136 in2
Answer:
52in^2
Step-by-step explanation:
The area of a triangle is A= 1/2bh
The area of a rectangle is A=lw
The top triangleThe base of the top triangle would be the length of the base of the two right triangles plus the length of the width of the the rectangle.
A=1/2bh
A=1/2(2+2+4)(4)
A=1/2(8)(4)
A=1/2(32)
A=16in^2
2. The two right triangles
A=1/2bh
A=1/2(2)(6)
A=1/2(12)
A=6in^2
(Because the two triangle are the same we just multiply the area by 2 to get the value of both)
A=12in^2
3. The rectangle
A=lw
A=6(4)
A=24in^2
-
Now just add the value of the areas for the different shapes.
16in^2 + 12in^2 + 24in^2 = 52in^2
If the nth partial sum of infinity n=1 an is given by Sn = 3n + 2/n + 3, what is an when n 2? an = 7/(n + 3)(n + 4) an = 7/(n + 3)(n + 2) an = 11/n(n + 3) an = 11/(n + 3)(n + 4) an = 11/(n + 3)(n + 2) an = 7/n(n + 3)
an = 7/n(n+3), when n ≥ 2.
To solve this problem, we need to use the formula for the nth partial sum of a series:
Sn = a1 + a2 + ... + an
where a1, a2, ..., an are the terms of the series up to the nth term. We are given that
Sn = 3n + 2/n + 3
so we can write
a1 = 3(1) + 2/1 + 3 = 5/4
a2 = 3(2) + 2/2 + 3 = 8/5
a3 = 3(3) + 2/3 + 3 = 11/6
and so on.
We can use partial fractions to rewrite Sn in terms of the individual terms an:
Sn = a1 + a2 + ... + an
= (7/12) - (7/(n+2)) + (7/(n+3)) - (7/(n+4))
= 7/n(n+3)
where we have used the fact that the partial sums are equal to the sum of the first n terms minus the sum of the first (n-1) terms.
Therefore, we have an = 7/n(n+3), when n ≥ 2.
To learn more about partial sum: https://brainly.com/question/29050520
#SPJ11
Please Urgent! 90pts + [tex]brainliest[/tex]
Shown in picture!
[tex]Expectations:[/tex]
Correct
Exaplantion
Reasonable
[tex]MUST[/tex] [tex]NOT[/tex]
Incorrect
Spam
Nonsense
No explanation
[tex]Thanks! [/tex]
From the picture, the rate of the increase can be obtained as 10 m/s^2.
What is the acceleration?Acceleration is the rate of change of velocity over time. It is a vector quantity, which means that it has both magnitude and direction. Acceleration can be positive, negative, or zero, depending on whether an object is speeding up, slowing down, or maintaining a constant velocity. The standard unit of acceleration is meters per second squared (m/s²) in the SI system, but other units like feet per second squared (ft/s²) or kilometers per hour squared (km/h²) may also be used.
Given that
F = ma
a = F/m
a = 50 N/5 Kg
a = 10 m/s^2
Learn more about acceleration:https://brainly.com/question/12550364
#SPJ1
