## Question

###### 1 6. The general form of a linear, homogeneous, second-order equation with constant coefficients is dy...

1 6. The general form of a linear, homogeneous, second-order equation with constant coefficients is dy dy form.

ns (b) Show that if q关0, then the origin is the only equilibrium point of the sys (c) Show, that if q关0, then the only solution of the second-order equation constant is y(t) = 0 for all 1.

## Answers

Given that d^2 y/d t^2 + p dy/dt + qy = 0 consider the 2nd order equation with constant coefficient d^2 y/d t^2 + p dy/dt + qy = 0 rightarrow 1 (a) The objective is to write the 1st order system for eq 1 and write this system in matrix form Assume that v = dy/dt du/dt = d^2 y/d t^2 = -p dy/dt - q y from 1 = -pv - qy Therefore The 1^st order system is dy/dt = v dv/dt = -pv - qy dy/dt = 0 + v dv/dt = -qy - pv \r\n The system in matrix form is [dy/dt dv/dt] = (0 -q 1 -p) (y v) dv/dt = Ay where A = (0 -q 1 -p): y = [y v] (b) The objective is to prove that the origin is the only equilibrium point of the system if q notequalto 0 consider the system dy/dt = Ay here A = (0 -q 1 -p) to find the equilibrium point, take

#### Similar Solved Questions

1 answers

##### Check [The following information applies to the questions displayed below.) At the beginning of 2018, Copeland...

Check [The following information applies to the questions displayed below.) At the beginning of 2018, Copeland Drugstore purchased a new computer system for $180,000. It is expected to have a five-year life and a $30,000 salvage value. Required a. Compute the depreciation for each of the five years,...

1 answers

##### Differential Analysis for Sales Promotion Proposal Sole Mates Inc. is planning a one-month campaign for July...

Differential Analysis for Sales Promotion Proposal Sole Mates Inc. is planning a one-month campaign for July to promote sales of one of its two shoe products. A total of $123,000 has been budgeted for advertising, contests, redeemable coupons, and other promotional activities. The following data hav...

1 answers

##### On December 31, 2016, Vaughn Inc. borrowed $3,360,000 at 13% payable annually to finance the construction...

On December 31, 2016, Vaughn Inc. borrowed $3,360,000 at 13% payable annually to finance the construction of a new building. In 2017, the company made the following expenditures related to this building: March 1, $403,200; June 1, $672,000; July 1, $1,680,000; December 1, $1,680,000. The building wa...

1 answers

##### A $1,000 par value bond has a current price of $884.94 and a maturity value of...

A $1,000 par value bond has a current price of $884.94 and a maturity value of $1,000 and matures in 6 years. If interest is paid semiannually and the bond is priced to yield 8%, what is the bond's annual coupon rate? The bond's annual coupon rate is (blank...

1 answers

##### Grant has 4 hours of time in all to divide between studying for a physics exam...

Grant has 4 hours of time in all to divide between studying for a physics exam and a geology exam. Table 1 shows his estimates of the grades (on a scale of o to 100) that he could eam from studying a particular number of hours on each subject. If he plans on spending two hours studying physics and t...

1 answers

##### Which of the following is not a good reason to offer for an acquisition? Multiple Choice...

Which of the following is not a good reason to offer for an acquisition? Multiple Choice 0/1 points awarded Scored ( ) It will diversify the firm's business risk. It will provide diseconomies of scale. It will decrease earnings per share. It will increase agency costs. It will increase the firm&...

1 answers

##### 6. Indicate the approximate sites of ac- tion for each of the following: azide, rotenone, antimycin...

6. Indicate the approximate sites of ac- tion for each of the following: azide, rotenone, antimycin How can you tell?...

1 answers

##### 9. P ropose a multi-step synthesis to accomplish the overall transformation shown below (make the molecule...

9. P ropose a multi-step synthesis to accomplish the overall transformation shown below (make the molecule on the right starting with the molecule on the left). Show all necessary reagents and products for each forward step. [It is not necessary to show any mechanisms.] OH 10. Propose a multi-step s...

1 answers

##### On January 2, 2019, Dekker Company grants each of its 15 new employees 200 restricted share...

On January 2, 2019, Dekker Company grants each of its 15 new employees 200 restricted share units. Each of the time-vested restricted share units entitles the employee to receive one share of Dekker common stock if they remain an employee of the company for 2 years. On January 2, 2019, shares of Dek...

1 answers

##### Many studies have been conducted to test the effects of marijuana use on mental abilities. In...

Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below: Items sorted correctly by light marijuana users: n = 64, x-bar = 53.3, s ...

1 answers

##### QUESTION 3 According to a newspaper 80% of 600 adults polled by telephone say they think...

QUESTION 3 According to a newspaper 80% of 600 adults polled by telephone say they think going to Mars is a good idea for the world. Find the 98% CI for the proportion of adults who think that going to Mars is a good investment for the world. Τ Τ Τ Τ Paragraph Arial SE 3 (12pt) E - E...

1 answers

##### Have started the patient on Ezembe Zeta A d anism of action of the drug? Who...

have started the patient on Ezembe Zeta A d anism of action of the drug? Who 25 m m Blocks cholesterol absorption sans Inhibits HMG-CoA reductase C Promote the oxidation of cholesterol to bile acids Intwibits lipoprotein lipase activity at hemos c o n 26 Nadia sell-administers pseudoephedrine for en...

1 answers

##### If oxygen gas in a steel container is at a pressure of 3.10 atm, what is...

If oxygen gas in a steel container is at a pressure of 3.10 atm, what is the pressure expressed in each of the following units? Part A mm Hg AO P= Submit Request A Part B psi | ΑΣΦ Submit Request Ans Provide Feedback...

1 answers

##### 8. A simple circuit is composed of an ideal 100 v battery in series with three resistors (R1 = 10Ω, R2 = 20Ω, R3 = 30Ω). Which of the following statements is true? Statement A: Each resistor carries t...

8. A simple circuit is composed of an ideal 100 v battery in series with three resistors (R1 = 10Ω, R2 = 20Ω, R3 = 30Ω). Which of the following statements is true? Statement A: Each resistor carries the same current. Statement B: Each resistor has the same voltage. Statement C: Eac...

1 answers

##### 1) Write complete reaction mechanisms for the formation of 1-bromobutane and also show how 1-butene and...

1) Write complete reaction mechanisms for the formation of 1-bromobutane and also show how 1-butene and di-n-butyl ether are formed. di-n-butyl ether =...

1 answers

##### I need help with C. I got wrong answers.It is not 7050 or 1218. I need tp use 13.4 table. Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior...

I need help with C. I got wrong answers.It is not 7050 or 1218. I need tp use 13.4 table. Fashionables is a franchisee of The UnLimited, the well-known retailer of fashionable clothing. Prior to the winter season, The UnLimited offers Fashionables the choice of five different colors of a par...

1 answers

##### 4) A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were divided randomly int...

4) A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were divided randomly into two groups. One group was asked to use the software program twice a day, once in the morning and once in...

1 answers

##### Factor f(x) = 3x + 10x4 104x + 64 into linear factors given that - 8...

Factor f(x) = 3x + 10x4 104x + 64 into linear factors given that - 8 is a zero of f(x). f(x) = 3x9 + 10x - 104x +64 = 1 (Factor completely.)...