Consider a particle that experiences the following two-dimensional acceleration: * = -kx = -2ky Find and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a particle that experiences the following two-dimensional acceleration: * = -kx = -2ky Find and sketch the path the particle takes by following the plan given below. Remember: the dot notation represents derivatives with respect to time. Plan: 1. Write each differential equation in the form: s+as+bs + c = 0. Which of the coefficients are zero? 2. Write down the characteristic equations for each differential equation. Remember: the characteristic equation takes the form: cr + cr + coro = 0. 3. Find the roots for each of your characteristic equations. 4. Use the roots to find the solution to each differential equation. 5. Use these initial conditions: at t = 0, (x,y) = (a,0) and x, y) = (0, yo) to find the constants of integration. 6. Use the result to sketch the path. Consider a particle that experiences the following two-dimensional acceleration: * = -kx = -2ky Find and sketch the path the particle takes by following the plan given below. Remember: the dot notation represents derivatives with respect to time. Plan: 1. Write each differential equation in the form: s+as+bs + c = 0. Which of the coefficients are zero? 2. Write down the characteristic equations for each differential equation. Remember: the characteristic equation takes the form: cr + cr + coro = 0. 3. Find the roots for each of your characteristic equations. 4. Use the roots to find the solution to each differential equation. 5. Use these initial conditions: at t = 0, (x,y) = (a,0) and x, y) = (0, yo) to find the constants of integration. 6. Use the result to sketch the path.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these physics questions
-
Find the average rate of change for the given function. f(x) = x + 2x between x = 0 and x=9
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
For the month ending September 30, 2020, Gardener Company has received $10,000 from customers, $30,000 in capital contributed from shareholders, and borrowed $20,000 from the bank. The company also...
-
Describe at least one method by which the organization can reduce change resistance?
-
What role does manufacturing play relative to the standard of living of a country?
-
At a rock concert, the sound intensity 1.0 m in front of the bank of loudspeakers is 0.10 W/m 2 . A fan is 30 m from the loudspeakers. Her eardrums have a diameter of 8.4 mm. How much sound energy is...
-
The program computes federal withholding tax for each employee by multiplying gross pay times a tax rate determined from Table 9-9. The program next computes state withholding tax for each employee...
-
Roehm Co. issued $30,000,000 of four-year, 10% bonds, with interest payable semiannually, at a market (effective) interest rate of 8%. Determine the present value of the bonds payable, using the...
-
Initial capital investment Estimated useful life Estimated disposal value in 3 years Estimated annual savings in cash operating costs(end of year) Minimum desired rate of return Present value of...
-
If the coefficient of static friction between all the surfaces of contact is s, determine the force P that must be applied to the wedge in order to lift the brace that supports the load F. N' PNA B....
-
Professor s Annuity Corporation offers a lifetime annuity to retiring professors. For a payment of $ 8 0 , 0 0 0 at age 6 5 , the firm will pay the retiring professor $ 6 0 0 a month until his death....
-
A 1370-kg car is skidding to a stop along a horizontal surface. The car decelerates from 27.6 m/s to a rest position in 3.15 seconds. Assuming negligible air resistance, determine the coefficient of...
-
Happy Place Designs makes custom backyard play structures that it sells to dealers across the Midwest. The play structures are produced in two departments, fabrication (a mostly automated department)...
-
If an electron with spin down in the Psi (9,1,0) eigenstate in a hydrogen atom. If you want to measure the total angular momentum squared (L^2) of the electron, what are the possible values that you...
-
Part (a) Find the total energy transferred to the photon to four significant figures. Assume the reactants are initially at rest. Use the following atomic mass values when determining the total...
-
Focus on the current makeup of the health care workforce, the challenges posed by shortages in certain professions, and how these shortages are being addressed. Most health care in the United States...
-
A Brooklyn College alumnus recently established an endowment fund that will provide annual scholarships of $12,000 for 25 years. The fund will pay the first scholarship in 5 years. The fund can earn...
-
To balance the chemical equation SiH3 + O2 SiO2 + HO, you could introduce coefficients a, b, c, d and write aSiH3 + bO2 cSiO + dHO then write linear equations for each element. The equation for Si...
-
(a) Find the acceleration of P.(b) Calculate the azimuthal force on a mass m located at P, and show that the result is consistent with part(a). Firans -m- Feent -mw x (w x r). Fcor = -2mw x v, dw Faz...
-
(a) Using the notation and initial conditions of the example in Section 8.7.6, and assuming ?3 >> ?? >> ?s, find (approximately) the direction of the angular momentum right after the sideways kick...
-
A double Atwood's machine is shown in Fig., with masses m1, m2, and what are the accelerations of themasses? , .
-
What are the factors that explain the difference in yields to maturity between long-term and short-term bonds?
-
If the yield to maturity on a two-year zero coupon bond is 13 per cent and the yield to maturity on a one year zero coupon bond is 10 per cent, what is the expected spot rate of one-year bonds in one...
-
You are considering three alternative investments in bonds. The bonds have different times to maturity, but carry the same default risk. You would like to gain an impression of the extent of price...
Study smarter with the SolutionInn App