Differential equation class. Please show steps to the solutions.
Differential equation class. Please show steps to the solutions. Section 3.3 Exercises To Solutions For all exercises...
Differential Equation class. Show the steps for the solutions please. Section 3.2 Exercises To Solutions 1. Suppose that the mass is set in motion by moving it upward by 2.5 cm and releasing it with no initial velocity (a) Sketch what you think the graph of y versus t will look like, taking care with the fact that positive y is upward. Make the amplitude of the motion clear on your graph. (b) Express the initial conditions mathematically by giving...
MATLAB HELP (a) Use the command dsolve to find general solutions to the differential equations below. i. y 00 + 3y = 0 ii. y 00 + 4y 0 + 29y = 0 iii. y 00 − y/36 = 0 iv. y 00 + 2y 0 + y = 0 v. y 00 + 6y 0 + 5y = 0 (b) Graph each of the solutions in (a) in the same window with 0 ≤ t ≤ 10, using the...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
This two problems go together 3. Write a program called VibratingSystem that does the following a. Takes the following as input i. Spring constant, k; ii. Mass under vibration, m; iii. Coefficient of viscous damping, c, iv. Initial position of the mass. xi, v. And initial velocity of the mass. vi b. If the values k or m are less than or equal to zero, ask for those variables again. c. Plot the results for t from 0 to 20...
This two problems go together 3. Write a program called VibratingSystem that does the following a. Takes the following as input i. Spring constant, k; ii. Mass under vibration, m; iii. Coefficient of viscous damping, c, iv. Initial position of the mass. xi, v. And initial velocity of the mass. vi b. If the values k or m are less than or equal to zero, ask for those variables again. c. Plot the results for t from 0 to 20...
answer please , Cauchy problem Exercise 4. Find all solutions of the following differential equation, after determining its domain sin y (-1) Moreover, find the solution to the Cauchy problem with initial data y(0) sketch its graph. Finally, study the behaviour of the function thus obtained at r determining its order of infinitesimal or infinite, if defined. 2 and 1 Exercise 4. Find all solutions of the following differential equation, after determining its domain sin y (-1) Moreover, find the...
1) Answer the following questions for harmonic oscillator with the given parameters and initial conditions Find the specific solution without converting to a linear system Convert to a linear system Find the eigenvalues and eigenvectors of the corresponding linear system Classify the oscillator (underdamped, overdamped, critically damped, undamped) (use technology to) Sketch the direction field and phase portrait Sketch the x(t)- and v(t)-graphs of the solution a. b. c. d. e. f. A) mass m-2, spring constant k 1, damping...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability of the equilibria you found in (a). (c) How does the solution with y(0) =-1 behave as t -» +00? How does the solution with y(0) 1 behave as t - --0? 3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability...
Differential Equation: Series Solutions Near an Ordinary point, find a0 to a7 in the power series for the solution of the IVP. In Exercises 19-28 find the coefficients ao. an for N at least 7 in the series solution n=0 of the initial value problem. Take xo to be the point where the initial conditions are imposed In Exercises 19-28 find the coefficients ao. an for N at least 7 in the series solution n=0 of the initial value problem....