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
Brut [27]
3 years ago
14

Use Routh's stability criterion to determine how many roots with positive real parts the following equations have:

Engineering
1 answer:
Pavlova-9 [17]3 years ago
3 0

Answer:

a) no roots not in LHP

b) 2 roots not in LHP

c) 2 roots not in the LHP

d) 2 roots not in the LHP

e) 2 roots not in LHP

Explanation:

a) s^4 + 8s^3 + 32s^2 + 80s + 100 = 0\\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:32\:\:\:\:\:\:100\\s^3:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\\s^2:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:100\\s^1:\:\:\:80-\frac{800}{22} =43.6\\s^0:\:\:\:100

No roots not in the LHP

b) s^5 + 10s^4 + 30s^3 + 80s^2+344s + 480 =0 \\\\s^5:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:30\:\:\:\:\:\:344\\s^4:\:\:\:10\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:480\\s^3:\:\:\:22\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:296\\s^2:\:\:\:-545\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:480\\s^1:\:\:\:490\\s^0:\:\:\:480

2 roots not in the LHP

c) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:7\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^3:\:\:\:2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:-2\\s^2:\:\:\:8\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:8\\s^1:\:\:\:-4\\s^0:\:\:\:8

There are roots in the RHP (not all coefficients are greater than 0).

2 roots not in the LHP

d) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^3:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:20\\s^2:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:78\\s^1:\:\:\:-58\\s^0:\:\:\:78

There are two sign changes in the first column of the Routh array.

2 roots not in the LHP

e) s^4 + 2s^3 + 7s^2 -2s + 8 = 0 \\\\s^4:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^3:\:\:\:4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:12\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: new \:\:row \\s^2:\:\:\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:25\\s^1:\:\:\:12-\frac{100}{3}=-21.3 \\s^0:\:\:\:25

2 roots not in LHP

check:

 a (s) = 0  ⇒

 s^2 = -3 \limits^+_- 4j = 5e^{j(\pi \limits^+_- 0.92)}\\\\s = \sqrt5 e^{j( \frac{\pi}{2} \limits^+_-  0.46)+n\pi j},\:\:\:\:\: n= 0, 1\\

You might be interested in
What makes building an airplane while flying so difficult?
Naddik [55]

Answer: Because if something goes wrong while you are flying it it will crash

Explanation:

7 0
2 years ago
Shear _______ can be directly computed from the angle of twist and the specimen dimensions. (a)- Stress (b)- Modulus (c)- Strain
fgiga [73]

Answer:

c) Strain

Explanation:

For example, the shear strain “γ” on the surface of the rod is determined by measuring the relative angle of  twist “φg” over a gage length “Lg”.

6 0
3 years ago
Air at 25ºC flows in an electric hair drier with a velocity of 6 m/s perpendicular to a Nichrome heating element. The heating el
Hunter-Best [27]

Answer:

Check the explanation

Explanation:

Electrical current can be measured according to the rate of electric charge flow in any electrical circuit:

i(t) = dQ(t) / dt

the derivative of the electric charge by time determines the momentary current.

i(t) will be the momentary current I at time t in amps (A).

Q(t) will also be the momentary electric charge in coulombs (C).

t is the time in seconds (s).

so if the current is constant:

I = ΔQ / Δt

I will be the current in amps (A).

ΔQ will be the electric charge in coulombs (C), which is expected to flows at time duration of Δt.

Δt is the time duration in seconds (s).

Kindly check the attached image below to get the step by step explanation to the question above.

3 0
3 years ago
A one-dimensional slab without heat generation has a thickness of 20 mm with surfaces main- tained at temperatures of 275 K and
vlada-n [284]

Answer:

a) 512.5 KW/m2

b) 40.75 KW/m2

c) 2 KW/m2

Explanation:

Given data;

T_2 = 325 K

T_1 = 275 K

dx = 0.20 mm

a) for aluminium   K = 205 W/m k

heat flux = k \frac{dt}{dx}

               = 205 \frac{325 - 275}{0.02}

               = 512.5 KW/m2

b) for AISI 316 stainless steel

k = 16.3 W/ m k

heat flux = k \frac{dt}{dx}

               = 16.3 \frac{325 - 275}{0.02}

               = 40.75 KW/m2

C) for Concrete

k = 0.8 W/ m k

heat flux = k \frac{dt}{dx}

               = 0.8 \times \frac{325 - 275}{0.02}

               = 2 KW/m2

6 0
3 years ago
Question 20) Which of the following materials has the greatest coefficient
s2008m [1.1K]

Answer:

Mild steel

Explanation:

all steel has the highest linear coefficient

6 0
2 years ago
Read 2 more answers
Other questions:
  • If link AB of the four-bar linkage has a constant counterclockwise angular velocity of 58 rad/s during an interval which include
    11·1 answer
  • A computer maintenance company wants to 'capture' the knowledge that employees carry around in their heads by creating a databas
    5·1 answer
  • Kirchoff's Law states that, by the time current has returned to its source, all
    13·2 answers
  • A large part in a turbine-generator unit operates near room temperature and is made of ASTM A470-8 steel ( ). A surface crack ha
    11·1 answer
  • You are given a partial implementation of one header file, GildedRose.hpp. Item is a class that holds the information for each i
    6·1 answer
  • Determine the total condensation rate of water vapor onto the front surface of a vertical plate that is 10 mm high and 1 m in th
    8·2 answers
  • Which of these parts of a cell phone is least likely to be found on the phone's circult board?
    5·1 answer
  • Is an example of an electrical device.
    13·2 answers
  • I need to solve for d
    11·2 answers
  • What is chemical engieering ?​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!